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

Answer:

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

Step-by-step 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

$\frac{1}{7} + \frac{1}{5} = \frac{1}{x}$

$\frac{5 + 7}{35} = \frac{1}{x}$

$\frac{12}{35} = \frac{1}{x}$

$12x = 35$

$x = \frac{35}{12}$

$x = 2.9167$

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.

Answer 2

Answer:

Step-by-step explanation:

WE can use the following formula:

$\frac{T}{X}+\frac{T}{Y}=1$

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:

$\frac{T}{7}+\frac{T}{5}=1\\\\\frac{12T}{35}=1\\\\T=(1)(\frac{35}{12})\\\\T=2.9167\ hours$

Since 1 hour has 60 minutes:

$(0.9167h)(\frac{60min}{1h})\\=55min$

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