Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels 5 km/h slower than the other. If the two cyclists are 78 kilometers apart after 2 hours, what is the rate of each cyclist?

Rate of the slower cyclist:
A. 36 km/h
B. 38 km/h
C. 40 km/h
D. 42 km/h

Answer 1

The rate of the slower cyclist is 17 km/h, and the rate of the faster cyclist is 22 km/h.

Step-by-step explanation:

To find the rates of the two cyclists, let's denote the rate of the slower cyclist as x km/h. Then, the rate of the faster cyclist would be x + 5 km/h, since the slower cyclist is traveling 5 km/h slower. After 2 hours, the total distance covered by both cyclists would be the sum of their distances. Since they are traveling in opposite directions, their distances would add up to 78 kilometers. Therefore, the equation would be:

2(x) + 2(x + 5) = 78

Simplifying this equation, we get:

4x + 10 = 78

Subtracting 10 from both sides, we get:

4x = 68

Dividing both sides by 4, we get:

x = 17

Therefore, the rate of the slower cyclist is 17 km/h, and the rate of the faster cyclist is 17 + 5 = 22 km/h.