Question

Two cyclists leave the same place going in the same direction. One cyclist travels 30 mph, and the second travels 35 mph. If the second cyclist starts 2 hours later than the first, in how many hours will the second overtake the first?

(a) 3 hours
(b) 4 hours
(c) 5 hours
(d) 6 hours

Answer 1

It takes the second cyclist 16 hours to overtake the first cyclist. None of the given options is answer.

Step-by-step explanation:

Let's assume the first cyclist has traveled for x hours. In that time, the first cyclist would have traveled 30x miles.

The second cyclist, starting 2 hours later, would have traveled for (x - 2) hours. In that time, the second cyclist would have traveled 35(x - 2) miles.

We know that the second cyclist overtakes the first cyclist when they have covered the same distance. Therefore, we can set up the equation:

30x = 35(x - 2)

Expanding the right side of the equation, we get:

30x = 35x - 70

Solving for x, we get:

5x = 70

x = 14

Therefore, the second cyclist overtakes the first cyclist after 14 hours. Since the second cyclist started 2 hours later, the total time it takes for the second cyclist to overtake the first cyclist is 14 + 2 = 16 hours. None of the given options is answer.