# Math World Problem (functions)?

If Sue and Bill work together on a job, they can do the job in 7 hours. If Bill works alone, it takes him 15 hours. Write an equation to find out how long the job would take Sue working alone.

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• If Sue and Bill work together on a job, they can do the job in 7 hours.

If Bill works alone, it takes him 15 hours.

1/15 + 1/x = 1/7

1/x = 8/105

8x = 105

The job would take Sue 13 1/8 hours working alone.

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• Unit of work per hour by Bill = W/15, where w is total units (the work).

Unit of work by both = W/7,

Unit of work by Sue = W/r, where h given no. of hours alone by Sue.

But, W/7 - W/r = W/15,

1/7 - 1/15 = 1/r,

r = 15*7/8 hours = 105/8 = 13 hour 07 min 30 s.

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• -

Let work to be done be A units

Combined rate = A/7 units/hour

rate for Bill = A/15 units/hour

rate for Sue = A/t units/hour

1/7 = 1/15 + 1/t

1/7 - 1/15 = 1/t

15/105 - 7/105 = 1/t

8/105 = 1/t

t = 105/8 = 13 h 7½ min______time for Sue working alone

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• If Sue and Bill work together on a job, they can do the job in 7 hours.

If Bill works alone, it takes him 15 hours.

1/7 - 1/15 = 1/s

15s - 7s = 105

8s = 105 h

s = 13 1/8 h

It would take Sue 13 h 7 m 30 s to do the job working alone.

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• a is the rate of work for Sue. b is the rate of work for bill, Work is 1

If they work together, the time is

1/(a+b)=7, 1/b=15. 1= 7(a+b), 1=15b, You have

15 b =7a+7b. 8b=7a, a=8/7 a = 8/105. Sue's working rate is 8/105

Check it.

a+b=1/15+8/105=15/105=1/7

1/7 work per day. 7 days to complete. For Sue along it will take 105/8 days. 13 +1/8 days.

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• Anonymous
7 months ago

simple formula for when both work alone are known

Sue*Bill / Sue+Bill

for when just one work alone is known (simple algebra)

Sue alone = Bill*both / Bill-both

15*7 / 15-7 = 105/8 (about 13 1/8 hours)

try it. you will like it

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• ....unit rates for Sue + Bill = 1 / 7 , while for Bill it is 1 / 15 ===> unit rate for Sue is ( 1 / 7 ) - ( 1 / 15) = 8 / 105 ===> Sue takes 105 / 8 = 13 1/8 hours

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