Problema Solution
Lance Armstrong can ride 162 miles on flat ground in 6 hours with a good breeze at his back. It takes him 10 hours to go 90 miles with the same breeze working against him. How fast is lance going on a bike and how fast is the wind speed?
Answer provided by our tutors
let
v = the speed of Lance without any wind, v>0
w = the wind speed, w>0
d1 = 162 miles the distance he travels with a good breeze at his back
t1 = 6 hours the time he travels with a good breeze at his back
d2 = 90 miles the distance he travels with the same breeze working against him
t2 = 10 hours the time he travels with the same breeze working against him
the speed of Lance with a good breeze at his back: v + w
the speed of Lance with the breeze working against him: v + w
since speed = distance/time follows distance = speed*time
traveling with a good breeze
d1 = t1(v + w)
t1(v + w) = d1
6(v + w) = 162 divide both sides by 6
v + w = 27
traveling with the same breeze working against him
d2 = t2(v - w)
t2(v - w) = d2
10(v - w) = 90 divide both sides by 10
v - w = 9
by solving the system of equations
v + w = 27
v - w = 9
we find
v = 18 mph
w = 9 mph
click here to see the step by step solution of the system of equations
the speed of lance without wind is 18 miles per hour.
the speed of the wind is 9 miles per hour.