Word problem..help please?

Question

Micheal and Peter pratise motocross racing. Michael completes one lap in 22s. Peter does 1 lap in 17 seconds. Michael gets a 176 s head start.

Write the rules expresing the number of laps completed by each racer in terms of the time since the race began.

Please help? This problem has me SO frustrated, even though it sounds so easy. So basically they are asking you for TWO equations dirived from the info.

Answer 1

Michael gets a 176 sec head start, and 176/22 = 8, so he has already done 8 laps when Peter starts. Therefore:

Michael laps = 8 + (time so far)/22
Peter laps = (time so far)/17

Peter will catch Michael when their laps are equal:

8 + x/22 = x/17
x = 598.4 sec

at which time, they both will have completed 35.2 laps

8 + 598.4/22 = 35.2 laps
598.4/17 = 35.2 laps

At least I think that is the answer, based on your question.

Answer 2

Let t=0 when Michael begins the race. Then at time t seconds Michael has completed

M = t/22 laps

Since Peter starts the race when t = 176, the formula for his number of laps completed makes sense only when t > 176. At time t > 176 Peter has completed

P = (t-176)/17 laps