Maths-

General

Easy

Question

# Three bricklayers, Maric, Hugh and Ethan, are cladding a new home. If Maric were to work alone, the job would take him 8 days to complete. If Hugh were to work alone, the job would take him 6 days to complete and if Ethan were to work by himself, the job would take him 12 days to complete. a) If the three men work together, how long will it take them to complete the job? b) What fraction of the house will each bricklayer complete?

Hint:

**Hint:**

When two quantities of different units are compared and expressed as a ratio, it is known as Rate. For example, a car travels at a speed of 100 kilometres per hour, then it means in one hour it covers 100 kilometres.

## The correct answer is: a) 2 2/3 , b)2/9

### Let’s say the work done to build the home is W and let’s say the work done by Maric in one day is W_{M}, work done by Hugh in one day is W_{H} and work done by Ethan in one day is W_{E}.

Step 1 of 2:

It is given that Maric builds the home in 8 days. So we can write

W_{M} × 8 = W

W_{M} = …….(1)

It is given that Hugh builds the home in 6 days. So we can write

W_{H} × 6 = W

W_{H} = …….(2)

It is given that Ethan builds the home in 12 days. So we can write

W_{E} 12 = W

W_{E} = …….(3)

Step 2 of 2:

Now, adding equations (1), (2) and (3)

W_{M} + W_{H} + W_{E} = + +

W_{M} + W_{H} + W_{E} = ……(4)

a)

From equation (4), we get to know that work is done by all three in one day.

So, the number of days required by all three to complete W work = = = days

Final Answer:

Hence, it would take days to build the house all the three men worked together.

b)

Work done by Maric in days = W_{M} × = × =

Work done by Hugh in days = W_{H} × = × =

Work done by Ethan in days = W_{E} × = × =

Final Answer:

Hence, Maric will build of the house, Hugh will of the house and Ethan will build of the house.

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