Math Is Fun Forum

coolboyx12

Member

Registered: 2023-03-10

Posts: 34

how do you solve this question?

Alice and Bob take 2 hours to complete a task, Alice and Charlie take 3 hours to complete a task and Bob and Charlie take 4 hours to complete a task, how much time will Alice, Bob and Charlie take to complete
that same task?

how do you solve this question.

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It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,136

Re: how do you solve this question?

hi coolboyx12

Elsewhere you said "Isn't one of the rules of this forum to not advertise products."  Yes you're right.  It has been dealt with, thanks.

Let's say that Alice can do A units of work per hour; Bob can do B units of work per hour and Charlie C units of work per hour.

Then when Alice and Bob are working together  they do 2A + 2B units of work = total units for task.

Similarly 3A + 3C also = total and lastly 4B + 4C is the same.

ie.  2A + 2B = 3A + 3C = 4B + 4C = T

So we have three equations and 4 unknowns.  Using simultaneous equation techniques you can express A in terms of T and similary B and C.

So finally create an equation for them all working together in x hours ... xA + xB + x C = T..
Sub in the values for A, B and C in terms of T, cancel the Ts and you're left with an equation for evaluating x.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

coolboyx12

Member

Registered: 2023-03-10

Posts: 34

Re: how do you solve this question?

Thanks Bob

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It pays to keep an open mind, but not so open your brains fall out. - Carl Sagan.