RATE
PROBLEMS
1. ds≠0
Column A : The time
required to travel d miles at s miles per hour
Column B : The time
required to travel d/2 miles at 2s miles per hour
2. Column A : The time that it takes Jim to drive
300 miles at a speed of 52 miles per hour.
Column B : The time
that it takes Lila to drive 240 miles at a speed of 40 miles per hour.
3. A distillate flows in to an empty 64 –gallon
drum at spout A and out of the drum at spout B. If the rate of flow through A
is 2 gallons per hour, how many gallons per hour must flow out at spout B so
that the drum is full in exactly 96 hours?
4. X > 0
Quantity A: 
Quantity
B: 
Quantity
B:
5. Column A : The total number of
liters of water in x tanks, each containing 20 liters of water, and
2x tanks , each containing 35 liters of water.
Column B : The total number of liters of water in x tanks , each containing 25
liters of water, and 2x tanks , each containing 30
liters of water.
6.
(1) Two tanks , X and Y, are filled to
capacity with jet fuel. Tank X holds 600 gallons more than Tank
Y. If 100 gallons of fuel were to be pumped
from each tank, tank X would then contain 3 times as much fuel as tank Y. What
is the total number of gallons of fuel in the two full tanks?
(A) 1,400 (B)
1,200 (C) 1,000 (D)
900 (E) 800
(2) A
certain machine fills a bag with 7 ounces of potato chips in 3.5 seconds. At
this rate how many seconds will it take the machine to fill a bag with 15
ounces of potato chips?
(A) 6.5 (B)
7.0 (C) 7.5 (D) 8.0 (E)
11.5
7. One bacterial cell of a certain type is placed
in a petri dish. Cells of this type divide once every day.
Column A : The total
number of bacterial cells in the dish at the end of 4 days if no cells die
Column B : 6
8. An aviator in Mexico flew 300 kilometers in a
straight line due east from point P to point Q and then 400 kilometers in a
straight line due north to point R .
Column A : The
shortest distance from point P to point
R Column B :
550 kilometers
x>0
9. Column A : The number of minutes in x+ 100
hours
Column B : The number
of seconds in 60(x+100) minutes
10. If a small juice contains 200 milliliters of
juice, how many liters of juice are there in a case containing 48 small cans?
(1 liter = 1,000 milliliters)
(A)
0.96 (B) 9.6 (C) 96
(D) 960 (E) 9,600
11. If a certain
object has been moving at the constant rate of x meters per minute, how many
meters has the object moved in the last y seconds?
(A) 
(B) 
(C) 
(D) 
(E) 60xy
(B) (C) (D) (E) 60xy
12. A secretary typed
6 letters, each of which had either 1 or 2 pages. If the secretary typed 10
pages in all, how many of the letters had 2 pages?
(A)
1 (B)
2 (C)3
(D) 4 (E) 5
13. At 9:00 a.m. train
T left the train station and two hours later train S left the same station on a
parallel track. If train T averaged 60 kilometers per hour and train S averaged
75 kilometers per hour until S passed T , at what time time did S pass T ?
(A) 2:00
p.m. (B) 5: 00
p.m. (C)6:00
p.m. (D) 7: 00
p.m. (E) 9:00 p.m.
14. Seven cars were
used to transport the members of a chess team to their match , and each car
contained either 4 team members or 3 team members.
Column A : The total
number of members on the chess team
Column B : 25
15. A train travels 60
miles per hour for 3 hours and then 45 miles per hour for 2 hours. What is the
train’s average speed in miles per hour during the 5-hour period?
(A)
1 (B)
2
(C)3 (D)
4 (E) 5
16. Two people were
hired to mow a lawn for a total of $45 . They completed the job with one person
working for 1 hour and 20 minutes and the other working 40 minutes. If they
split the $45 in proportion to the amount of time each spent working on the
job, how much did the person who worked longer receive?
(A) $33.75 (B)
$30.00 (C)
$27.50
(D)$25.00 (E) $22.50
17. In a certain
country , a person is born every 3 seconds and a person dies every 10 seconds.
Therefore , the birth and death rates account for a population growth rate of
one person every
(A) 3 
sec
(B) 4 sec
(C) 7 sec (D) 11 
sec
(E) 13 sec
sec
(B) 4 sec
(C) 7 sec (D) 11 sec
(E) 13 sec
18. The price of a pen
is (10x + y ) cents, the price of a notebook is (10y + x ) cents, and the sum
of the two prices is $1.43.
Column A :
x
Column B : y
19. If 15 pies cost a total of $11.50 , then at
this rate , what is the cost of 9 pies?
(A) $6.75
(B) $ 6.90 (C)
$7.50
(D)$8.50 (E) $9.45
20. At the rate of 3,000 revolutions per minute ,
how many revolutions will a wheel make in k seconds ?
21. On map X
each centimeter represents 20 kilometers.
Column A : The actual
distance, in kilometers, between two locations that are 17 centimeters
apart on map X
Column B : 300
21. Pencils have the same unit unit cost
regardless of the number sold. x pencils cost a total of $0.50 , and n pencils
cost a total of y dollars.
Column A
:n
Column B : 2xy
22. The daily rate for a hotel room that sleeps 4
people is $39 for one person and x dollars for each additional person. If
3 people take the room for one day and each pays $21 for the room , what is the
value of x?
(A)
6 (B)
8
(C)12 (D) 13
(E) 24
23. If a person
can save $380 in 5 weeks , in how many weeks, at this same rate , can the
person save 2.6 times this amount?
(A)
13 (B)
12.5 (C)
11 (D)
10.6 (E) 8
24. A car travelling
at a constant sped of 50 miles per hour k gallons of fuel each hour .
Column A : The number
of gallons of fuel this car uses to travel 200 miles at a constant speed of 50
miles per hour.
Column B : 4k
25. A buzzer sounds
every 15 minutes. If the buzzer sounded at 12:40 , which of the following could
be a time at which the buzzer sounded?
(A) 4:
05 (B) 5: 30
(C) 6: 45 (D) 7:
15 (E) 8: 10
26. A cyclist
travels x miles in w hours and z minutes.What is the cyclist’s speed in miles
per hour?
27. Maria purchased 3
pounds of candy X for $ 7.98 and 5 pounds of candy Y for $10.95.
Column A : The price
Maria paid per pound for candy X
Column B :
The price Maria paid per pound for candy Y
28. A student can
purchase a research report for $5.00, or reproduce the x pages of the report at
accost of $0.15 per page.
Column A : The
greatest possible value of x if the cost of reproducing the x pages is less
than the cost of purchasing the report
Column B : 34
29. Column A : The
cost of x apples at a cost of y + 2 cents a piece
Column B : The cost of y oranges at a cost of x + 2 cents a piece
30. A watch gains 7
minutes and 6 seconds every 6 days. If the rate of gain is constant , how much
does the watch gain in one day?
(A) 1 min 1 sec
(B) 1 min 6 sec (C) 1min 11 sec (D) 1 min 16 sec (E) 1
min 21 sec
31. The distance from
point X to point Y is 20 miles, and the distance from point X to point Z is 12
miles. If d is the distance , in miles, between points Y and Z , then the range
of possible values for d is indicated by
(A) 8 ≤ d ≤
20 (B) 8 ≤ d ≤ 32 (C)12 ≤
d ≤ 20 (D) 12 ≤ d ≤ 32 (E)
20 ≤ d ≤ 32
32. A machine packages milk at the rate of q
quarts per hour.
Column A : The number of hours required
for the machine to package 5,000 quarts of milk
Column B : 8
33. The cost of 48 cans of soda is $20 .
Column A : At the same rate, the cost,
in dollars, of n of these cans of soda
Column B : (0.24)n
34. A manufacturer packages soap powder in
containers of three different sizes. The amount of soap powder in a full large
container could fit exactly 3 of the medium containers or exactly 5 of the
small containers . If an equal number of small and large containers are to be
filled with the amount of soap powder that would fill 90 medium containers, how
many small containers will be filled?
(A)
25 (B)
27 (C)
30 (D)
45 (E) 54
35. Each of the
following numbers has two digits blotted out. Which of the numbers could be the
number of hours in x days, where x is an integer?
(A) 25- , -
06 (B) 50- ,
-26 (C)
56-,-02 (D)
62-,-50 (E) 65-,-20
36. Team X scored 10
points in the first half of a certain game . In the second half of the game,
team Y scored 15 points more than team X .
Column A : The
number of points scored by team X I the first half of the game
Column B : The number
of points scored by team Y I the first half of the game.
37. Column A :
The cost of x pounds of meat at y dollars per pound
Column B : The
cost of y yards of material at x dollars per yard
38. Column A
: The cost per gram of carrots if 3 cans of carrots cost $0.90
Column B : The cost
per gram of onions if 5 cans of onions cost $1.50
39. A certain car gets
24 miles per gallon of gasoline for city driving, which is 60 % of the number
of miles per gallon of gasoline the car gets for highway driving.
Column A : The
number of gallons of gasoline used to drive this car 30 miles in the city
Column B
: The number of gallons of gasoline used to drive this car 45
miles on the highway
40. Column A
: The number of minutes in y weeks
Column B : The number of hours in 60y weeks
41. A certain
writer noted that , on an average , 3 pages of a manuscript were equivalent to
1 page of the published book. If the writer has a 302-page manuscript , about
how many pages will the published book have ?
(A)100
(B)
150 (C)
300 (D)
600 (E) 900\
42. The Acme Rent- a-
car agency charges $10.00 per day and $0.10 per mile to rent a car. The super
Rent-a- car agency charges $20.00 per day and $0.05 per mile to rent a car . If
a car is rented for 1 day, at how many miles would the rental charges of the
two agencies be equal?
(A)
50 (B)
100 (C)
150 (D)
175 (E) 200
43. When Fred
drives from his home to the nearest mountain resort, it takes 4 hours at an
average speed of 50 miles per hour. When Fred drives from his home to beach
house , it takes 3.5 hours at an average speed of 55 miles per hour.
Column A :
Fred’s driving distance from his home to the nearest mountain resort
Column B :
Fred’s driving distance from his home to his beach house
44. At a grocery store
Ray paid $1.85 for 5 pounds of potatoes and $1.29 for 3 pounds of apples.
Column A : The
amount Ray paid per pound for the potatoes
Column B : The amount
Ray paid per pound for the apples
45. A certain form
letter is to be sent to prospective customers .If 4 model-X computers working
independently can do a combined total of 4 of the letters in 4 minutes,
then 100 model-X computers working independently can do a combined total
of 100 of the letters in exactly how many minutes?
(A) 4
min (B) 10
min (C) 25
min (D) 40
min (E) 100 min
46. Column A :
The number of minutes in y weeks
Column B :
The number of hours in 60y weeks
47. A train travels
from C ity X to City Y in 3 hours and 30 minutes at an average speed of 60
miles per hour. If the train returns at an average speed of 50 miles per hour,
how long does the return trip take ?
(A) 2 hr 55
min (B) 3 hr 40 min (C) 4 hr 12
min (D) 4 hr 32 min (E) 4 hr 40 min
48. A certain store
sells each pencil at the same price regardless of the number of pencils sold. K
of these pencils have a total price of q cents , and r of these pencils
have a total price of s cents.
Column A :
ks
Column B : qr
49. If 18 identical
machines required 40 days to complete a job, how many fewer days would have
been required to do the job if 6 additional machines of the same type had been
used from the beginning?
(A)
10 (B) 13 (C)
16 (D) 26 (E) 36
(C)
16 (D) 26 (E) 36
49. Toni bought n
dozen eggs for $12 and m half gallons of milk for $6.
Column A : The
price Toni paid for a dozen eggs
Column B : The
price Toni paid for a half gallon of milk
50. A printer numbered
consecutively the pages of a book, beginning with 1 on the first page .In
numbering the pages , he printed a total of 189 digits.
Column A : The number
of pages in the book
Column B : 100
51. When walking
, a certain person takes 16 complete steps in 10 seconds. At this rate, how
many complete steps does the person take in 72 seconds?
(A)
45 (B)
78 (C)
86 (D)
99 (E) 115
52. Working at
constant rates , machine R completely presses x records in 0.5 hour and machine
S completely presses x records in 0.75 hour( x > 0)
Column A : The number
of records completely pressed by R in 3 hours .
Column B : The
number of records completely pressed by S in 4 hours .
53. A spraying machine
uses 5 full gallon buckets of fungicide every 20 minutes.
Column A: The number
of gallons of fungicide the machine uses during 8 hours of spraying .
Column B : 720
54. A contractor can
purchase paint at $19.50 per gallon or at the bulk rate of 20 gallons for
$335.00
Column A: The amount
saved per gallon by purchasing 20 gallons of the paint at the bulk rate rather
than by the gallon
Column B: $2.75
55. A school district
has 1,989 computers, which is approximately one computer for every 68.6
students. Of the following , which is the closest approximation of students in
the school district?
(A)
30 (B)
120 (C)
140 (D)
160 (E) 200
56. An emergency
vehicle travels 10 miles at a speed of 50 miles per hour. How fast must
the vehicle on the return trip if the round- trip travel time Is to be 20
minutes?
(A) 55
mph (B) 60 mph (C) 65 mph
(D) 70 mph (E) 75 mph
57. For each of
n people, Margie bought a hamburger and a soda at a restaurant .For each of n
people, Paul bought 3 hamburgers and a soda at the same restaurant. If Margie
spent a total of $5.40 and Paul spent a total of $12.60 , how much did Paul
spent just for hamburgers ? (Assume that all hamburgers cost the same and
all sodas cost the same .)
(A) $
10.80 (B) $ 9.60 (C) $7.20
(D) $3.60 (E) $2.40
58. If a certain
company purchased its computer terminals for a total of $40,400 and each of the
terminals was purchased for $350 , how many terminals did the company purchase?
(A)
1,624 (B) 1,544
(C) 1,434
(D) 1,384 (E) 1,264
59. x copies of
sports magazine X cost a total of $12.
Column A : The total
cost, in dollars, of m copies of fashion magazine M
Column B : 100
60. Sue drives 10
miles from home to work. If she could average 50 miles per hour , how many
minutes would it take her to drive from home to work?
(A)
20 (B) 18 (C)
15 (D) 12 (E) 10
61. Column A : The
number of minutes it takes a car going 50 miles an hour to go 30 miles
Column B : The number of seconds it takes a car going 50
miles an hour to go 30 miles
62. A
time-study specialist has set the production rate for each worker on a certain
job at 22 units every 3 hours. At this rate what is the minimum number of
workers that should be put on the job if atleast 90 units are to be produced
per hour?
(A) 5
(B) 8
(C) 12
(D) 13 (E) 30
63 . Column A :
The number of hours to travel 1,500 miles at an average speed of 400
miles per hour.
Column B : The number
of hours required to travel 200 miles at an average speed of 50 miles per hour
64. Column A : The number of shares of stock
X purchased for $1,581,000
Column B : The
number of shares of stock Y purchased for $1,603,000
65. A certain photocopying machine can make 10
copies every 4 seconds. At this rate , how many copies can the machine make in
6 minutes?
(A) 900 (B)
600 (C) 360 (D)
240 (E) 150
66. Worker W produces n units 5 hours. Workers
V and W , working independently but at the same time ,
produce n units in 2 hours. How long would it take V alone to produce n units?
(A) 1 hr 26 min (B)
1 hr 53min (C) 2 hr 30 min (D) 3 hr 20
min (E) 3 hr 30 min
67. Andy
earns $5 per hour.
Susan earns $6 per hour.
Column A : The amount
Andy earns in 6
hours.
hours.
Column B :
The amount Susan earns in 5 hours.
hours.
68. The cost of strawberries is $0.45 per pint if
piced by the customer and $1.25 per quart already picked(2 pints = 1 quart)
Column A : The cost of
8 quarts of strawberries picked by the customer.
Column B : The cost of
6 quarts of strawberries already picked
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