Posted by **Taylor** on Monday, January 24, 2011 at 9:24pm.

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.

- math -
**helper**, Monday, January 24, 2011 at 9:59pm
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.

- math -
**Taylor**, Monday, January 24, 2011 at 11:14pm
Why did you add -4s + -2.5s ?

- math -
**helper**, Monday, January 24, 2011 at 11:22pm
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

- math -
**Taylor**, Monday, January 24, 2011 at 11:27pm
Okay, I understand now, thanks!

- math -
**helper**, Monday, January 24, 2011 at 11:45pm
You're welcome!

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