Question 331844
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/4}}} + {{{(5d)/16}}} = {{{(6d)/a}}}
multiply equation by 16a, to eliminate the denominators, results
:
4ad + 5ad = 16(6d)
9ad = 96d
divide both sides by d
9a = 96
a = {{{96/9}}}
a = 10{{{2/3}}} 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
{{{5/4}}} + {{{25/16}}} = {{{30/10.67}}}
1.25 + 1.5625 = 2.8125; confirms our solution