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Time and work
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
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1 Reply
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Let’s assume that the amount of work to be done is represented by “W.”
We are given the following information:
A can do the work in 4 hours, so A’s work rate is 1/4W per hour.
B and C together can do the work in 3 hours, so their combined work rate is 1/3W per hour.
A and C together can do the work in 2 hours, so their combined work rate is 1/2W per hour.
To find B’s work rate, we need to subtract A’s work rate and C’s work rate from the combined work rate of B and C.
Let’s say B’s work rate is represented by “b” (per hour) and C’s work rate is represented by “c” (per hour).
The combined work rate of B and C is b + c = 1/3W per hour.
The combined work rate of A and C is 1/2W per hour.
We know A’s work rate is 1/4W per hour. So, A’s work rate plus C’s work rate is 1/4W + c = 1/2W per hour.
Now, we can set up two equations to solve for b and c:
A’s work rate plus C’s work rate: 1/4W + c = 1/2W
Combined work rate of B and C: b + c = 1/3W
Let’s solve these equations:
1/4W + c = 1/2W
c = 1/2W – 1/4W
c = 1/4W
b + c = 1/3W
b + 1/4W = 1/3W
b = 1/3W – 1/4W
b = 1/12W
From the equation, we can see that B’s work rate is 1/12W per hour. This means that B alone can complete the work in 12 hours.
Therefore, B alone will take 12 hours to do the work.
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