Question

IT takes chris 9 hours longer to construct a fence than it take tony. If they work together, they caan construct the fence in 20 hours. How long would it take each man working alone?

Answer 1

Tony: 36 hours

Chris: 45 hours

EXPLANATION

If it takes Tony x hours to construct the fence, then it will take Chris (x+9) hours.

Tony's rate is

`(1)/(x)`

Chris' rate is

`(1)/(x + 9)`

Their combined rate in terms of x is

`(1)/(x) + (1)/(x + 9)`

Their combined rate must equal

`(1)/(20)`

This implies that;

`(x + 9 + x)/(x(x + 9)) = (1)/(20)`

`(2x + 9 )/(x(x + 9)) = (1)/(20)`

Cross multiply,

`x(x + 9) = 20(2x + 9)`

Expand;

`{x}^(2) + 9x = 40x + 180`

This implies that,

`{x}^(2) + 9x - 40x - 180 = 0`

`{x}^(2) - 31x - 180 = 0`

`{x}^(2) - 36x + 5x - 180 = 0`

`(x - 36)(x + 5) = 0`

`x = 36 \: or \: x = - 5`

We discard the negative value.

Hence

`x = 36`

Therefore it will take Tony 36 hours and Chris 45 hours.

Answer 2

Tony = 36 Hours

Chris = 45 Hours

Explanation:

let y+9 = Chris's time to build the fence alone

let y = Tony's time

let the completed job = 1

20/y+9 + 20/y = 1

Multiply the equation by y(y+9)

20y + 20(y+180) = y(y+9)

20y + 20y + 180 = y^2 + 9y

40 y + 180 = y^2 + 9y

0 = y^2 + 9y -40y - 180

y^2 - 31y - 180

(y + 5)(y - 36) = 0

y + 5 = 0

y = 0 - 5

y = -5 We reject this answer since we're only interested in the positive answer in terms of work done by two people.

y - 36 = 0

y = 0 + 36

y = 36 hours

So Chris takes y + 9 hours more than Tony

Chris's Time = y + 9

Chris's Time = 36 + 9

Chris's Time = 45 hours