Question

14. Two cyclists make the same trip. The first one takes 3.5 hours and the second, with a
speed that is 1 km/h greater than that of the first, takes 3 hours. Find the speeds of the two
cyclists. Also, find the distance covered in the trip.​

Answer 1

Answer:

Cyclist A is travelling at 10 kmph.

Cyclist B is travelling at 15 kmph.

Obviously, Cyclist A will take a longer time than Cyclist B to cover the same distance.

Let the distance covered by A and B be d km.

Time taken by B = 1 km/15 kmph = 4 min/km. So he takes 4d minutes, total.

Time taken by A = 1 km/10 kmph = 6 min/km. So he takes 6d minutes, total.

Now 6d-4d = 2d = 40 minutes, or d = 20 km.

So A and B cover 20 km on their cycles.

Check: A takes 20 km/10 kmph = 2 hours = 120 min.

B takes 20 km/15 kmph = 1.33 hours = 80 min.

So A takes 40 min more than A to cover 20 km. Correct.