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Activity Discussion Math Time and work

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• # Time and work

Posted by on June 23, 2023 at 12:21 am

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?

replied 3 months, 1 week ago 2 Members · 1 Reply
• ### Ayush

Member
June 23, 2023 at 1:41 am
0

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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