Problema Solution
An athlete walks one mile, then runs the second mile and cycles the third mile.
He runs twice as fast as he walks and he cycles one and a half times as fast as he runs.
He takes 10 minutes longer than he would do if he cycled the 3 miles.
How long does he take by walking, running and cycling?
Answer provided by our tutors
let
v1 = the walking speed
v2 = the running speed
v3 = the cycling speed
He runs twice as fast as he walks
v2 = 2v1
he cycles one and a half times as fast as he runs
v3 = 1.5v2
v3 = 1.5*2*v1
V3 = 3*v1
He takes 10 minutes longer than he would do if he cycled the 3 miles:
we use the formula time = distance/speed
1/v1 + 1/v2 + 1/v3 = 3/v3 + 10/60
1/v1 + 1/v2 + 1/v3 = 3/v3 + 1/6
plug v2 = 2v1 and V3 = 3*v1 into the last equation
1/v1 + 1/(2v1) + 1/(3v1) = 3/(3v1) + 1/6
1/v1 + 1/(2v1) + 1/(3v1) = 1/v1 + 1/6
1/v1 + 1/(2v1) + 1/(3v1) - 1/v1 = 1/6
(1/v1)(1/2 + 1/3) = 1/6
(1/v1)(5/6) = 1/6 multiply both sides by 6/5
1/v1 = 1/5
v1 = 5 mph
v2 = 2*5 = 10 mph
v3 = 3*5 = 15 mph
he walks: 1/5 hr = 60/5 = 12 min
he runs: 1/10 hr = 60/10 = 6 min
he is cycling: 1/15 hr =60/15 = 4 min