Question

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Maggie can do a job in 15 hours less than Ryan can. If they work together they can get the job done in 10 hours. How long would it take cach to do the job alone?
Maggie can do the job in
hours
Ryan can do the job in
hours

Answer 1

Maggie = 15 hours

Ryan = 30 hours

Explanation:

let x - time it takes Ryan to do the job alone.

x-15 - time it takes Maggie to do the job alone

`(10)/(x) + (10)/(x - 15) = 1 \\ \\ (10(x - 5) + 10x)/(x(x - 15)) = 1`

`10x - 150 + 10x = x {}^(2) - 15x \\ \\ 20x - 150 = x {}^(2) - 15x \\ \\ x {}^(2) - 15x - 20x + 150 = 0 \\ \\ x {}^(2) - 35x + 150 = 0 \\ \\ (x - 30)(x - 5) = 0 \\ \\ x = 30 \: and \: x - 15 = 15`

x = 5 --> not valid because x-15 will be NEGATIVE

Therfore,

Maggie can do the job in 15 hours.

Ryan can do the job in 30 hours.