   SEARCH HOME Math Central Quandaries & Queries  Question from bevaz: A and B can together do a piece of work in 6 days, B and C together in 20 days and C and A in 7.5 days. how long will they require separately for the work? Bevaz,

Go to the Quandaries and Queries page on Math Central and use the Quick Search to search for the term working together to see how we have approached these problems. Yours is slightly more involved because of the three people but the idea is still the same.

I can get you started. Suppose A can complete the job in a days, B in b days and C in c days, then the rates at which they work are 1/a, 1/b and 1/c jobs/day. Hence A and B working together work at a rate of 1/a + 1/b jobs/day. Thus the amount of time they take for a job is days.

But we know this is 6 days so days.

Now look at the other two pairings. If you need more assistance write back.

Penny

Bevaz wrote back

so, a + b = 6 days
b + c = 20

Bevaz,

For the equation I would first multiply both sides by to get .

Writing the left side with the common denominator ab this equation becomes

6a + 6b = ab.

Now look at the other pairs, A with C and B with C.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.