Work rate - technicians building server

[lind0923]

Hi All,
I'm having trouble figuring out how to set up this work rate problem. Can someone please give me some guidance? Thanks so much!


13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women and boys)?
a) 42
b) 54
c) 21
d) 63
e) 24

answer: [spoiler]a)42[/spoiler]

[Ian Stewart]

Hi All,
I'm having trouble figuring out how to set up this work rate problem. Can someone please give me some guidance? Thanks so much!


13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women and boys)?
a) 42
b) 54
c) 21
d) 63
e) 24

answer: [spoiler]a)42[/spoiler]

One could use a formula for a problem like this, but any combined rates problem can be answered if you rewrite all of your information using the same amount of time (rather than the same number of jobs, which is usually how the information is provided). So, here, for example, if 13 men and 7 boys complete 1 job in 7 days, they'll complete 6 jobs in 42 days (if they spend six times longer working, they'll do six times the work). Using this logic for both pieces of information:

13 men and 7 boys can finish 6 jobs in 42 days
6 boys and 13 women can finish 7 jobs in 42 days.
13 men, 13 boys and 13 women can finish 13 jobs in 42 days.
1 man, 1 boy and 1 woman can finish 1 job in 42 days.

(for the last line, using the fact that 1/13th the number of workers will do 1/13th as much work).

[quocbao]

Wow, your answer is quite elegant

Thanks Ian