math
posted by Taylor .
In a motorcycle race, one lap of the course is 650 m. At the start of the race, John sets off 4 seconds after Tom does, but John drives his motorcycle 5m/s faster and finishes the lap 2.5 seconds sooner than Tom does.
What is the speed at which each of them is driving?
What is the time taken by each of them to cover the distance.

RT = D
T = time for Tom
T  6.5 = time for John (4s + 2.5s)
R = rate for Tom
R + 5 = rate for John
D = 650
RT = D
RT = 650
(R + 5)(T  6.5) = 650
Solve these equations simultaneously.
Expand (R + 5)(T  6.5) = 650
Then substitute, RT = 650 for RT in the expansion. 
Why did you add 4s + 2.5s ?

John sets off 4 seconds after Tom does, and finishes the lap 2.5 seconds sooner than Tom does.
So, John's total time will be 6.5 sec less than Tom's time.
Do you understand?
Also, If you solved correctly, R = 20 and T = 32.5.
Remember, the problem wants each racers' speed and time.
So use the below to calculate that after you solve the equations for T and R.
T = time for Tom
R = rate for Tom
T  6.5 = time for John
R + 5 = rate for John 
Okay, I understand now, thanks!

You're welcome!