Question

Two cyclists leave towns 130 kilometers apart at the same time and travel toward each other. One cyclist travels 5 km/h faster than the other.If they meet in 2 hours, what is the rate of each cyclist?

Answer 1

Faster cyclist = 37.5km/h

Slower cyclist = 32.5km/h

Explanation:

Let's call the rate of the slower cyclist "r" (in km/h). Then the rate of the faster cyclist is "r+5" (in km/h), since they are traveling 5 km/h faster.

We know that the two cyclists are traveling towards each other and will meet in 2 hours. We can use the formula:

distance = rate × time

Let's call the distance each cyclist travels "d". Since they are traveling towards each other, their distances will add up to the total distance between the two towns, which is 130 km. So we can write:

d + d = 130

2d = 130

d = 65

Now we can use the formula again to find the rates of the two cyclists:

For the slower cyclist:

distance = rate × time

65 = r × 2

r = 32.5 km/h

For the faster cyclist:

distance = rate × time

65 = (r+5) × 2

r+5 = 32.5 + 5 = 37.5 km/h

So the rate of the slower cyclist is 32.5 km/h, and the rate of the faster cyclist is 37.5 km/h.