Two trains running in the same direction on the same track travel at the rates of 40 and 45 mph,
respectively. If the slower train starts out an hour earlier, how long will it take the faster train to catch
up with i
...
Two trains running in the same direction on the same track travel at the rates of 40 and 45 mph,
respectively. If the slower train starts out an hour earlier, how long will it take the faster train to catch
up with it?
a. 5 hours
b. 6 hours
c. 7 hours
d. 8 hours - ✔✔-d. 8 hours
The slower train is 40 miles ahead in one hour. The difference in rate is 5 mph, and 40/5=8
A naval detachment has enough rations to feed fifteen people for 8 days. If five more people join the
detachment, for how many fewer days will the rations last?
a. 1
b. 2
c. 3
d. 4 - ✔✔-b. 2
Let x = the number of ration days for 20 persons.
15×8=20xx
20x=120
x=120/20
x=6 ration days for 20 persons.
Therefore 8 days - 6 days = 2 days fewer.
A field can be plowed by 12 machines in 7 hours. If 4 machines are broken and cannot be used, how
many hours will it take to plow the field?
a. 7 1/2 hours
b. 8 1/2 hours
c. 9 1/2 hours
d. 10 1/2 hours - ✔✔-d. 10 1/2 hours
Let x equal the number of hours to plow with 8 machines. So,
12×7=8xx
8x=84
x=84/8
x=10 1/2 hours
What is the square root of 4 raised to the fifth power?
a. 8
b. 16
c. 32
d. 64 - ✔✔-c. 32
√4=2
2⁵=2×2×2×2×2
=32
If 3n - 2 = 27, what does n equal?
a. 5
b. 7
c. 8
d. 12 - ✔✔-a. 5
3^n-²=27
3³=27
n-2=3
+2 +2
n =5
If the sum of the edges of a cube is 24 inches, what is the volume of the cube?
a. 4 cubic inches
b. 8 cubic inches
c. 16 cubic inches
d. 64 cubic inches - ✔✔-b. 8 cubic inches
A cube has 12 edges, so each edge is 24/12=2
Volume=length x width x height
V=2×2×2
v=8
How much pure acid must be added to 10 ounces of a 55% acid solution in order to produce a 75% acid
solution?
a. 5 ounces
b. 6 ounces
c. 7 ounces
d. 8 ounces - ✔✔-d. 8 ounces
Pure Acid
-No. of Ounces : x
-Parts Pure Acid
: 100
-No. of Ounces of
Pure Acid : 100x
40% Acid Solution
-No. of Ounces : 10
-Parts Pure Acid
: 55
-No. of Ounces of
Pure Acid : 550
60% Acid Solution
-No. of Ounces : 10 + x
-Parts Pure Acid
: 75
-No. of Ounces of
Pure Acid : 75(10 + x)
100x+550=75(10+x)
100x+550=750+75x
-75x-550-550-75x
25x=200
x=8
A farmer who is 6 feet tall wants to determine the height of his barn. He notices that his shadow is 14
feet long and that his barn casts a shadow 70 feet long. How high is the barn?
a. 30 feet
b. 35 feet
c. 40 feet
d. 45 feet - ✔✔-a. 30 feet
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