Download MAT 1033 Section 8 5 distance rate time and work related word

MAT 1033
Section 8.5
APPLICATIONS OF RATIONAL EXPRESSIONS
Work Related Problems
1. Phil can do a job in 6 hours, but Steve can do the same job in 4 hours. How long will it
take them to do the job working together?
2. Wilma can do a job in 5 hours, whereas Stella needs 9 hours to do the same job. How
many hours will it take them to do the job working together?
3. Alexander can do a job in 3 hours. It takes Leopold 11 hours to do the same job. How
long will Alexander and Leopold need to do the job if they work together?
4. Katie can do a job in 7 hours. When Katie and Latasha work together, they can do the
job in 3 hours. How long would Latasha need to do the job if she worked alone?
5. Mario and Ashish can do a job in 8 hours if they work together. Working by himself,
Ashish could do the job in 12 hours. How long would Mario need to do the job working
alone?
6. Chen Singh can do a job in 4 hours, while Fred needs 5 hours to do the same job. How
long would Chen Singh and Fred require to do the job working together?
7. Desdamona needs 6 hours to do a job. If she works together with Hypatia, they can get
the job done in 2 hours. How long would Hypatia take to do the job if she worked by
herself?
8. Two robots, R2D2 and C3PO, can do a job in 9 hours. Working by itself, R2D2 can get
the job done in 15 hours. How long would C3PO need to do the job working by itself?
Answers:
2
1. 2 hours
5
5. 24 hours
2. 3
3
hours
14
6. 2
2
hours
9
3. 2
5
hours
14
7. 3 hours
4. 5
1
hours
4
8. 22
1
hours
2
MAT 1033
Section 8.5
APPLICATIONS OF RATIONAL EXPRESSIONS
Distance, Rate, and Time
1. Kate averages 10 miles per hour riding her bike to town. Averaging 30 miles per hour by car takes
her 2 hours less time. How far does she travel to town?
2. Emily’s boat goes 14 miles per hour. Find the speed of the current in the river if she can go 8 miles
downstream in the same time as she can go 6 miles upstream.
3. Lauren’s boat can go 9 miles per hour in still water. How far downstream can Lauren go if the river
has a current of 3 miles per hour and she must be back in 4 hours.
4. A canal has a current of 2 miles per hour. Find the speed of Leroy’s boat in still water if it goes 30
miles downstream in the same time as it takes to go 18 miles upstream.
5. Wilmoth can fly his plane 180 miles against the wind in the same time it takes him to fly 540 miles
with the wind. The wind blows at 30 miles per hour. Find the speed of his plane in still air.
6. Pauline and Pete agree to meet in Columbia. Pauline travels 120 miles, while Pete travels 80 miles.
If Pauline’s speed is 20 miles per hour greater than Pete’s and they both spend the same amount of
time traveling, at what speed does each travel?
7. Tim traveled from here to Bristol at 20 miles per hour and from Bristol to here at 60 miles per hour.
If the total time was 4 hours, how far is it from here to Bristol?
8. A river has a current of 3 kilometers per hour. Find the speed of Jena’s boat in still water if she
travels 60 kilometers downstream in the same time as 36 kilometers upstream.
9. Leo can get to the lake using either the old road at 40 miles per hour, or the new road at 60 miles per
hour. If both roads are the same length and he gets there 1 hour sooner on the new road, how far is it
to the lake?
10. Olivia can ride her bike 4 miles per hour faster than Ted. If Olivia can go 30 miles in the same time
that Ted can go 15 miles, what are their speeds?
Answer Key:
1. 30 mi
2. 2 mph
3. 16 mi
4. 8 mph
5. 60 mph
6. Pauline: 60 mph; Pete: 40 mph
7. 60 mi
8. 12 km/hr
9. 120 mi
10. Ted: 4 mph; Olivia: 8 mph