SOLUTION: A cyclist who walks up the hills, rides 5 times as fast as he walks. If he cycles at 16 k.m/h and walks at 4 k.m/h then find his average speed over journey.

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Question 331844: A cyclist who walks up the hills, rides 5 times as fast as he walks. If he cycles at 16 k.m/h and walks at 4 k.m/h then find his average speed over journey.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
In order for this problem to make sense, I changed the word "fast" to "far"
:
A cyclist who walks up the hills, rides 5 times as far as he walks.
If he cycles at 16 k.m/h and walks at 4 k.m/h then find his average speed over journey.
:
Let a = his average speed
:
let d = distance he walked
and
5d = distance he rode
then
6d = total distance
:
Write a time equation; Time = dist/speed
:
walk time + cycle time = total time
d%2F4 + %285d%29%2F16 = %286d%29%2Fa
multiply equation by 16a, to eliminate the denominators, results
:
4ad + 5ad = 16(6d)
9ad = 96d
divide both sides by d
9a = 96
a = 96%2F9
a = 102%2F3 km/hr is his average speed
:
:
check solution by finding a value for d, assume d=5 km
he rode 25 km, walked 5 km, total 30 km
5%2F4 + 25%2F16 = 30%2F10.67
1.25 + 1.5625 = 2.8125; confirms our solution