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Rational Work Problems Quiz

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Rational Work Problems Quiz

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Algebraic rate-work problems

Created by

NELLIE ABAD
NELLIE ABAD
Philippines

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Rational Work Problems Quiz
 

Rational Work Problems QuizOnline version

Algebraic rate-work problems

by NELLIE ABAD
1

A can do a job in 6 hours, B in 8 hours. Working together for 3 hours, what fraction of the job is left?

2

A can do a job in 9 hours, B in 6 hours. Together, how long to finish one job?

3

A finishes in 5 hours, B in 7 hours. They work together until 60% of the job is done. How long did they work?

4

A can finish in 3 hours, B in 5 hours. They work together for 1 hour. What fraction remains?

5

A takes 4 hours, B takes 6 hours. They work until 3/4 of the job is done. How many hours did they work?

6

Three workers have rates 1/6, 1/9, and 1/12 per hour. How long for 1 job?

7

A finishes in 8 hours, B in 12 hours. They work together until 3/4 of the job is done. How long did they work?

8

A’s rate is 1/8 per hour, B’s rate is 1/12 per hour. How long to finish 1 job together?

9

A’s rate is x hours per job (1/x per hour), B’s rate is 6 hours per job (1/6 per hour). If together they finish in 3 hours, find x.

10

Three workers have rates 1/4, 1/5, and 1/10 per hour. How long for 1 job?

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Their combined rate is 1/6+1/8=7/24 per hour; in 3 hours they do 7/8, leaving 1/8.

Rate is 1/9+1/6=5/18 per hour; time = 1/(5/18)=18/5=3.6 hours? (Oops) Correct rate: 1/9+1/6=5/18, time = 18/5 = 3.6 hours. Correction: The correct value is 18/5 hours.

Combined rate = 1/5+1/7=12/35 per hour. Time = 0.6/(12/35)=1.75 hours.

Work done in 1 hour = 1/3+1/5=8/15. Remaining 1-8/15=7/15.

Combined rate = 1/4+1/6=5/12 per hour. Time = (3/4)/(5/12)=9/5=1.8.

Sum = 13/36 per hour; time = 1/(13/36)=36/13 hours.

Combined rate = 1/8+1/12=5/24 per hour. Time to 3/4 = (3/4)/(5/24)=18/5=3.6 hours.

Sum rates = 5/24 per hour; time = 1/(5/24)=24/5=4.8 hours. Correction: The correct time is 24/5 hours.

1/x+1/6=1/3 => 1/x=1/6 => x=6.

Sum = 11/20 per hour; time = 1/(11/20)=20/11 hours.

 
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