Question

Jackson can remove the shingles off of a house in 7 hours, while Martin can remove the shingles in 5 hours. How long will it

take them to remove the shingles if they work together?




The answer is t= 2 hours and 55 minutes

Answer 1

Explanation:

WE can use the following formula:

`(T)/(X)+(T)/(Y)=1`

Where "T" is the time time working together,

"X" the time for person X working alone and

"Y" is the time for person Y working alone.

Based on the data given in the exercise, we can identify that:

`X=7\\Y=5`

substituting these values into the formula and solving for "T", we get that this is:

`(T)/(7)+(T)/(5)=1\\\\(12T)/(35)=1\\\\T=(1)((35)/(12))\\\\T=2.9167\ hours`

Since 1 hour has 60 minutes:

`(0.9167h)((60min)/(1h))\\=55min`

Therefore, if they work together, it will take them 2 hours and 55 minutes to remove the shingles.

Answer 2

It will take them 2 hours and 55 minutes to remove the shingles if they work together.

Explanation:

The together rate is the sum of each separate rate.

In this problem:

Jackson's rate is 1/7

Martin's rate is 1/5.

The together rate is 1/x, which is what we want to find.

So

`(1)/(7) + (1)/(5) = (1)/(x)`

`(5 + 7)/(35) = (1)/(x)`

`(12)/(35) = (1)/(x)`

`12x = 35`

`x = (35)/(12)`

`x = 2.9167`

So 2 hours plus 0.9167 of an hour.

An hour has 60 minutes.

0.9167*60 = 55 minutes

So it will take them 2 hours and 55 minutes to remove the shingles if they work together.