1. A bus trip of 90 miles would have taken an hour less if the average speed had been
increased by 3 miles per hour. Find the usual average speed of the bus.
2. One pipe can fill a tank in 3 hours. With a second pipe also in operation the tank
can be filled in 2 hours. How long would it take the second pipe alone to fill the tank?
3. A Roman 40-oar galley rows 33 miles from Icaria to Samos with the wind in 1 and 1/2
hours. If the ship returns in 4 1/8 hours, what is the speed of the wind?
4. After making a trip of 126 miles, a man found that if he had increased his average
speed by 8 miles per hour, he could have made the trip in 1 hours less time. Find his
original rate.
5. To accommodate its members who were attending a convention, a society hired space in
a hotel for $360. When 6 members could not attend, however, each members had to be taxed
$2 more to provide the $360. How many members attended?
6. The teacher and students of an American Government class are to share the $540
expenses of a special bus trip to Washington, D.C. When 5 students were unable to go, the
cost per person was $1.50 greater. How many people made the trip?
7. Two numbers are in the ratio 6:11. If the first number is decreased by 4 and the
second is increased by 6, the resulting numbers are in the ration 4:9. Find the original
numbers.
8. If 2 is added to the numerator of a fraction, the value of the fraction becomes 1/2.
If 2 is subtracted from the numerator of the original fraction, the value of the fraction
becomes 1/6. Find the original fraction.
9. A fraction equals 8/9. The numerator is 2 more that 6 times the quotient of the
denominator and 7. Find the reciprocal of the original fraction.
10. If a number is increased by 4 times it's reciprocal, the sum is 41/6.
Find the number.
11. Working alone, a mechanic can do a job in 6 hours, but her helper needs 15 hours
when he works alone. Together they do the job when the helper works twice as long as the
mechanic. How long does each work when they do the job together?
12. A cafeteria strike was settled when busboys earning $72 per week were given a
salary increase of 20 cents per hour. As a result, each busboy worked four hours fewer
each week for the same salary. Before receiving his hourly increase, how many hours did
each work a week?
13. A crew times itself on a three-mile course. The three miles upstream takes 20
minutes, and the three miles downstream takes 12 minutes. Find the rate of the crew in
still water.
14. With the wind behind her, a skater crossed a frozen river 1 mile wide in 3 minutes.
She skated straight into the wind on her return trip which took 15 minutes. Find the speed
of the wind.
15. Working alone, Chuck, Mary and Steve can shovel the snow from Mr. Elder’s
driveway in 4, 3, and 6 hours respectively. How long will it take them when they work
together?
16. A carpenter can build a shed in 6 hours, but his apprentice needs 16 hours to do
the same job. When they work together to build the shed, the apprentice works 5 hours more
than the carpenter. How long does each work?
ANSWERS: 1. 15
mph 2. 6 hours 3. 7 mph 4. 28 mph 5. 30 people 6. 40 7. 36, 66 8. 8/3, 3/2 9. 63/56 10.
8/3, 3/2 11. 10/3, 20/3 2. 40 13. 12 mph 14. 8 mph 15. 4/3 hr 16. carpenter: 3,
apprentice: 8
MQ5 home Quiz
5 Test 6