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 ofthe 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 of2 miles per hour. Find the speed of Leroy's boat in still water ifit 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 kmlhr
9.120 mi
10. Ted: 4 mph; Olivia: 8 mph
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