Question

Sunny runs at a steady rate, and Moonbeam runs m times as fast, where m is a number greater than 1. If Moonbeam run to overtake Sunny a head start of h meteres, how many meters must Moonbeam run to overtake Sunny? ( Give your ansewr as an expression in terms of h and m.)

Hint : Let s be Sunny's rate. In terms of m and s, at what rate does Moonbeam catch up to Sunny?

Answer 1

4 hours

Step-by-step :

If Sunny runs twice as fast as Moonbeam

Given the assumed data:

Sunny's speed = 12m/h

Moonbeam's speed= 6m/h

Therefore, if they run for 2 hours, Sunny would have covered 12 * 2 = 24 miles

While Moonbeam would have covered 6 *2 = 12 miles in the same 2 hours.

This given illustration shows that given that all parameters are equal, except the x2 speed of Sunny to that of Moonbeam, he would always be 2x faster than Moonbeam.

If they run for 4 hours, Sunny would have covered 12 * 4 = 48 miles

While Moonbeam would have covered 6 *4 = 24 miles in the same 4 hours.