find the speed of each racer.

Question

Suppose the winner of a 600 mile car race finishes 12 minutes ahead of the second
place finisher. If the winner drives 5 miles per hour faster than the second racer, find the
speed of each racer.

Answer 1

600 = R(T - 1/5)

 

600 = (R-5)(T)

 

R(T-1/5) = (R-5)T

 

RT - (1/5)R = RT - 5T

 

Subtracting RT from both sides, and then multiplying by -1:

 (1/5)R = 5T

 

R = 25T

 

600 = (25T)(T - 1/5)

 

24 = T(T - 1/5)

 

0 = T(T - 1/5) - 24

 

0 = T^2 - (1/5)T - 24

 

0 =  5T^2 - T - 120

 

0 = ( 5T     +   24  )( T  - 5      )

 

 

5T + 24 = 0 results in negative times

 

T-5 = 0  ---> T=5

 

 

 

Plugging into the second equation:

 600 = (R-5)*5

 

120 = R-5

 

R = 125

 

 

T = 600/125 = 24/5 = 4 and 4/5 hr = 4 hours and 48 minutes which is 12 minutes faster

 

Faster car: 125 mph for 4 hours and 48 mins = 4 and 4/5 hr

 

2nd place car: 120 mph for 45 hours