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

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 9:59pmTom'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 10:07pmOOPS!

Please disregard the 2nd (bottom)procedure.

- math -
**Henry**, Thursday, January 27, 2011 at 11:47amAlternate 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.

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