Question

Ruiz can do a job in 5 hours. Carlos can do the same job in 8 hours. How many hours will it take the two of them to do the job if they work together?

Answer 1

it will take 3.08 hours to complete the job

Step-by-step explanation:

Ruiz can do a job in 5 hours

In 1 hour = 1/5 of the job would be completed

Carlos can do same job in 8 hours

In 1 hour = 1/8 of the job would be completed

let the Amount of time it takes both to complete = y

In 1 hr = 1/y of the job would be completed

The time it takes both to complete the job:

Amount of job Ruiz complete in 1 hr + Amount of job Carlos complete in 1hr = Amount of time it takes both to complete the job in 1 hr

`\begin{gathered} (1)/(5)\text{ + }(1)/(8)\text{ = }(1)/(y) \\ \frac{8(1)\text{ + 5(1)}}{40}\text{ = }(1)/(y) \\ \frac{8\text{ + 5}}{40}\text{ = }(1)/(y) \end{gathered}`
`\begin{gathered} (13)/(40)\text{ = }(1)/(y) \\ \text{cross multiply:} \\ 13(y)\text{ = 1(40)} \\ 13y\text{ = 40} \end{gathered}`
`\begin{gathered} \text{divide both sides by 13:} \\ y\text{ = }(40)/(13) \\ y\text{ = 3.08} \end{gathered}`

Hence, it will take 3.08 hours to complete the job