SOLUTION: A bicyclist rode into the country for 5h. In returning, her speed was 5mi/h faster and the trip took 4h. What was her speed each way?

Question 78559: A bicyclist rode into the country for 5h. In returning, her speed was 5mi/h faster and the trip took 4h. What was her speed each way?
Answer by patrickr(1) (Show Source): You can put this solution on YOUR website!
Use D = rt (Distance = rate * time) to solve.

The distance is the same each way, a fact we will use later.
The time riding into the country and back are given, 5 and 4.

Her speed(rate)riding into the country is unknown so we assign it a variable: s
Her time riding into the country is 5 hours.
D1=rt , plug s (her speed) in for r and 5 in for time.
D1=s*5

Her speed(rate) returning is 5mi/h faster that her speed riding in: Thus s+5
Her time riding into the country is 4 hours.
D2=rt , plug s+5 (her speed) in for r and 4 in for time.
D2=(s+5)*4

We know the two distances are the same, meaning D1=D2.
Substitute for D1 and D2 5s = 4(s+5)
Distribute the 4 5s = 4s+ 20
Subtract 4s from both sides s=20
Thus, her speed into the country was 20mi/h.
Her speed returning (5mi/h faster) was 25 mi/h.
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