I need help on a system of equations question.

Question

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 1

Let Lance velocity be v₁ and wind velocity be v₂ 

We have two cases:

1. Lance is riding with the wind:  v₁ + v₂ =162/6   (1)

2. Opposite: v₁ -v₂ = 162/10   (2)

Solving (1) and (2) results in:

v₁ = 21.6  MPH, and

v₂ = 5.4 MPH