Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels 6 km/h faster than the other. If the two cyclists are 120 km apart after 3 hours, what is the rate of each cyclist?

Answer 1

Answer: 17 and 23.

Explanation: Let the rate of the slower cyclist be x.

After 3 hours, the total distance between the both will be of:

3x (distance from the slower cyclist from the starting point) + 3(x + 6) (distance from the faster cyclist from the starting point) = 120.

Solving by x, 17 = x. Since x is the rate of the slowest cyclist, x + 6 = 23, is was the rate of the faster cyclist.

Answer 2

Let v is the rate of cyclist 1 and v + 6 is the rate of cyclist 2.

Equation: d = (v + v + 6) * t

Solving for v and v+6

d = (v + v + 6) * t

120 = (2v + 6)3

40 = 2v +6

2v=34

v = 17 km/h ………… is the rate of cyclist 1

v + 27 = 23 km/h…….. is the rate of cyclist 2