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.
7 Answers
 sepiaLv 72 months ago
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.
 Geeganage WLv 52 months ago
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.
 ComoLv 72 months ago

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
 KrishnamurthyLv 72 months ago
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.
 What do you think of the answers? You can sign in to give your opinion on the answer.
 VamanLv 72 months ago
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.
 SteveRenoLv 42 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 / Billboth
15*7 / 157 = 105/8 (about 13 1/8 hours)
try it. you will like it
 ted sLv 72 months ago
....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