Help with this word prob. 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.

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

b) Who would win the race if it consisted of 30 laps?

So by looking at b) you understand that there has to be someplace in both of the 2 equations that you make from question a) to put (number of laps) so that is obviously one of your variables.

Anyway, if anyone could help with these questions, it would be extremly appreciated. Thank you.

Answer 1

Number of laps = L
Time = T

a)
L[Michael] = T/22
L[Peter] = (T - 176)/17

b)
L[Michael] = T/22 so L[Michael] * 22 = T
L[Peter] = (T - 176)/17 so L[Peter] * 17 = (T - 176) so L[Peter] * 17 + 176 = T
Put 30 in place of L in both equations.

30 * 22 = T. T = 660 seconds to do 30 laps
30 * 17 + 176 = T. T = 686 seconds to do 30 laps

Michael would win a 30 lap race by 26 seconds

Answer 2

If we assume that the race started at T=0 seconds, (and that Peter started 176 seconds later), then:

a) The rule for expressing the number of laps completed by each racer after T seconds:

NLAP_Michael = T/22
NLAP_Peter = (T-176)/17

b) Substituting 30 laps into NLAP_Michael, and NLAP_Peter above and solving for T, yields the stopwatch time at which each racer completes 30 laps:

T_Michael(30) = 660 seconds,
T_Peter(30) = 686 seconds

Thus, Michael won, although Peter made up all but 26 seconds of his 176 second deficit.

Answer 3

a) L ( # of laps completed) = T( Time in seconds) / 22
for Michael
L ( #of laps completed) = T( Time in seconds) / 17; for Peter

b) Solving (T +176) / 22 = 30 for T tell us the time it takes Michael to complete the race given the conditions that he completes a lap in 22 seconds, assuming he does so at constant velocity.
T + 176 = 660
T = 484 seconds

Solving T/ 17 = 30 gives Peter total time with the same assumptions.
T = 510

Thus, Michael wins by 26 seconds. ( The cheater. . .)

Answer 4

a. Let t = seconds elapsed since the race begins

Michael's completed laps = t/22
Peter's completed laps = (t-176)/17

b. Determine how much time each racer takes to complete 30 laps

M = t/22
30 = t/22
t = 660 seconds for Mike to finish 30 laps

P = (t-176)/17
30 = (t-176)/17
t-176 = 510
t = 686 seconds for Peter to finish 30 laps

Therefore, MIKE WINS THE 30-LAP RACE by 26 seconds.

Answer 5

t = time in seconds elapsed since race started

Mlaps = t/22
Plaps = (t - 176)/17

if # laps = 30, for Michael
30 = t/22, so t=(30x22) = 660 sec

for Peter
30 = (t-176)/17
(t-176) = (30x17) = 510
t = 510 + 176 = 686 sec

Michael would win, since in comparing times 660 < 686.