## Week 11 Review: Answers and Solutions

Below are the solutions to the exercises and about work problems.

Problem 1
Aria can do a job in 7 days. What part of the job is finished after she worked for 3 days?

Aria can do a job in 7 days. So meaning, she can do 1/7 job each day.

1st day – 1/7
2nd day – 1/7
3rd day – 1/7

So, 3(1/7) = 3/7

Problem 2
Katya can do a job in 5 days. Marie can do the same job in 6 days. If they both worked for 1 day, what part of the job is finished?

Katya can do a job in 5 days which means each day 1/5 of the job.
Marie can do a job in 6 days which means each day 1/6 of the job.

Let x = part of the job finished for 1 day

1/5 + 1/6 = 1/x
LCD: 30x

Multiplying both sides of the equation by 30, we have
(30x)(1/5 + 1/6) = (30x)(1/x)
(30x/5) + 30x(1/6) = (30x/x)
6x + 5x = 30
11x = 30
x = 30/11 or 2 8/11

Problem 3
Ramon can paint a house in 6 days. Ralph can do the same job in 10 days. If they both worked for 2 days, what part of the job is done if they were to work together the whole time?

Ramon = 6 days (or 1/6 part each day)
Ralph = 10 days (or 1/10 part each day)

Let w – part of the job done for 2 days

w = 2(1/6) + 2(1/10)
w = 2/6 + 2/10

LCD: 30

30(2/6 + 2/10)
((30/6)*2)/30 + ((30/10)*2)/30
(5*2)/30 + (3*2)/30
10/30 + 6/30
16/30 or 8/15

8/15 – work done for 2 days.

If they were to worked together, they will finish the work in x days using the equation

1/6 + 1/10 = 1/x

We multiply both sides of the equation which is 30x giving us

30x(1/6) + 30x(1/10) = 30x(1/x)
(30x)/6 + (30x)/10 = (30x/x)
5x + 3x = 30
8x = 30
x = 30/8
x = 15/4

This means that both of them will finish the work in 15/4 days. This means that the amount of worked finished is (8/15)/(15/4) = (8/15)(4/15) = 32/225.

Problem 4
One hose can fill a pool in 3 hours and a smaller hose can fill the same pool in 4 hours. How long will it take the two hoses to fill the entire pool?

Let x – total time to fill the pool

1/3 + 1/4 = 1/x
LCD: 12x

Multiplying both sides by 12x, we have

12x(1/3 + 1/4 = 1/x)12
(12x)/3 + (12x)/4 = 12
4x + 3x = 12
7x = 12
x = 12/7 or 1 5/7 hours

Problem 5
Marco can dig a ditch in 5 hours and he and Jimmy can do it in 2 hours. How long would it take Jimmy to dig the same ditch alone?

Let 1/x – Jimmy’s time alone
1/5 – Marco’s time

1/x + 1/5 = 1/2
LCD: 10x
10x(1/x + 1/5) = (10x)(1/2)
10 + 2x = 5x
2x – 5x = -10
-3x = -10
x = -10/-3 or 3 1/3 hrs

Problem 6
Maria can paint a fence in 6 days and Leonora can do the same job in 7 days. They start to paint it together, but after two days, Leonora left, and Maria finishes the job alone. How many days will it take Leonora to finish the job?

Job done by Maria in 2 days = 2/6
Job done by Leonora in 2 days = 2/7
Job done by Maria in the remaining days = x/6

2/6 + 2/7 + x/6 = 1

LCD:42x

Multiplying both sides of the equation by 42, we have

42(2/6 + 2/7 + x/6) = (42)(1)
84/6 + 84/7 + (42x)/6 = 42
14 + 12 + 7x = 42
26 + 7x = 42
7x = 42 – 26
7x = 16
x = 16/7 or 2 2/7 days

Problem 7
An inlet pipe can fill a pool in 4 hours. An outlet pipe can fill the same pool in 6 hours. One day, the pool was empty. The owner opened the inlet pipe but forgot to close the outlet pipe. How long will it take to fill the pool?

Let x – hours to fill the pool
1/4 – 1/6 = 1/x
LCD: 12x

(12x)(1/4) – (12x)(1/6) = (12x)(1/x)
(12x)/4 – (12x)/6 = (12x)/x
3x – 2x = 12
x = 12 hours

## How to Solve Work Problems Part 3

This is the third part of the Solving Work Problems Series. The first part of this series discussed in detail the concept behind work problems and the second part discussed the basic work problems and their solutions.

In this post, we discuss two more work problems. The first problem is about two persons who started to work together and after a while, the other person stopped. The second problem is about filling a pool whose outlet pipe is left open.

Sample Problem 4

Jack can dig a ditch alone in 5 days, while John alone can do it in 8 days. The two of them started working together, but after two days, Jack left the job. How many more days do John need to work to finish the job alone?  » Read more