SOLUTION: Jake cycled 20 km to the beach. He returned cycling 1 km/h faster. The total time for the round trip was 9 h. Find his rate for each part of the trip.

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Question 242547: Jake cycled 20 km to the beach. He returned cycling 1 km/h faster. The total time for the round trip was 9 h. Find his rate for each part of the trip.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Jake cycled 20 km to the beach. He returned cycling 1 km/h faster.
The total time for the round trip was 9 h.
Find his rate for each part of the trip.
:
Let r = rate to the beach
then
(r+1) = rate from the beach
:
Write a time equation: time = dist/rate
:
To time + from time = 9 hrs
20%2Fr + 20%2F%28r%2B1%29 = 9
Multiply by r(r+1), results:
20(r+1) + 20r = 9r(r+1)
:
20r + 20 + 20r = 9r^2 + 9r
:
40r + 20 = 9r^2 + 9r
:
0 = 9r^2 + 9r - 40r - 20
:
9r^2 - 31r - 20 = 0
Factors to
(9r+5)(r-4) = 0
positive solution
r = 4 km/hr to the beach
then
5 km/hr from the beach
:
:
Check solution
20/4 + 20/5 = 9