System Equations

Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels 8 kmh faster than the other. If the two cyclists are 186 kilometers apart after 3 hours, what is the rate of each cyclist?

Answer 1

d = rt; t =3 hrs; d₁ + d₂ = 186

d₁= r₁t; d₂ = r₂t We know that r₂ = r₁ + 8

r₁t + r₂t = 186; factor out the t: t(r₁ + r₂) = 186

Substitute: t(r₁+ r₁ + 8) = 186 → 3(2r₁ + 8) = 186 → 2r₁ + 8 = 186/3 = 62

2r₁ = 54; r₁ = 27 kmph. Then r₂ = 35 kmph.

Check: 3(27) + 3(35) = 81 + 105 = 186