Posted by **Taylor** on Monday, January 24, 2011 at 9:17pm.

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 -
**Henry**, Wednesday, January 26, 2011 at 9:59pm
Tom's speed = X m/s.

John's speed = (X + 5) m/s.

Tom's time = Ys.

John's time=(Y - 2.5)S.

Eq1: X*Y = 650m.

Y = 650/X.

Eq2:(X + 5)(Y - 2.5) = 650m.

In Eq2, substitute 650/X for Y:

(X + 5)(650/X - 2.5) = 650,

650 - 2.5X + 3250/X -12.5 = 650,

650 - 2.5X + 3250/X - 12.5 -650 = 0,

-2.5X + 3250/X -12.5 = 0,

Multiply each side by -X:

2.5X^2 - 3250 + 12.5X = 0,

Divide each side by 2.5:

X^2 + 5X - 1300 = 0,

Solve for X using Quad.Formula and get:

X = 33.64; X = -38.64.

Select positive value of X:

X = 33.64m/s = Tom's speed.

X*Y = 650,

33.64Y = 650,

Y = 19.3s = Tom's time.

X + 5 = 33.64 + 5 = 38.64m/s = John's

speed.

John's time = Y - 2.5 = 19.3 - 2.5 -

16.8S.

X - 20 = 0,

X + 25 =0,

X = -25.

Choose the positive solution:

X = 20m/s = Tom's speed.

X + 5 = 20 + 5 = 25m/s = John's speed.

XY = 650,

20Y = 650,

Y = 650 / 20 = 32.5s. = Tom's time.

Y -6.5 = 32.5 - 6.5=26s. = John's time.

;

- math -
**Henry**, Wednesday, January 26, 2011 at 10:07pm
OOPS!

Please disregard the 2nd (bottom)procedure.

- math -
**Henry**, Thursday, January 27, 2011 at 11:47am
Alternate Approach:

Tom's speed = X m/s.

Tom's time = Ys.

John's speed = (X + 5)m/s.

John's time = Y - 2.5 - 4 = Y - 6.5.

Eq1: XY = 650m. Y = 650/X.

Eq2: (X + 5)(Y - 6.5) = 6.5m.

Substitute 650/X for Y in Eq2:

(X + 5)(650/X - 6.5) = 650,

650 - 6.5X + 3250/X - 32.5 = 650,

650 - 6.5X + 3250/X -32.5 -650 = 0,

-6.5X + 3250/X -32.5 = 0,

Multiply each side by -X:

6.5X^2 - 3250 + 32.5X = 0,

Divide each term by 6.5:

X^2 + 5X - 500 = 0,

(X - 20)(X + 25) = 0,

X - 29 = 0,

X = 20.

X + 25 = 0,

X = -25.

Select positive value of X:

Tom's speed = X = 20m/s.

XY = 650,

20^Y = 650,

Tom's time = Y = 650/20 = 32.5s.

John's speed = X + 5 = 20 + 5 = 25m/s.

John's time = 32.5 - 2.5 = 30s.

## Answer This Question

## Related Questions

- math - In a motorcycle race, one lap of the course is 650 m. At the start of the...
- math - motorcycle race 1 lape=750m. at the start gina sets off 4 sec. after tom ...
- math - john and tom race around a circular track,divided like the face of a ...
- maths - In a 1000 m race, John's speed is 25% faster than Jack's. The time John ...
- math - John I'd running in a race. The race is 25miles long. After two hours, ...
- Biomechanics - John and Al are in a 15 km race. John averages 4.4 m/s during the...
- Basic Biomechanics - John and Al are in a 15 km race. John averages 4.4 m/s ...
- ENGLISH - In which sentence is race used as a noun? A. Tom will race with four ...
- Acceleration physics - 1. A sprinter finishes the race with a velocity of 8.9 m/...
- physics - A race car completes the final lap of a race on a 2-kilometer circular...

More Related Questions