Question

Tom and Sam can finish a plowing job in two hours. Tom working alone can do the job in 7 hours. How long would it take Sam to finish the same job alone?

Answer 1

Solution:

Time taken by both Sam and Tom together = 2 hours

Time taken by Tom to work alone = 7 hours

Time taken by Sam to work alone = x hours [Let]

Rate of work done by both to do work in 1 hour = 1/2 job/hr

Rate of work done by Sam to do work in 1 hour = 1/7 job/hr

Rate of work done by Tom to do work in 1 hour = 1/x job/hr

Sam and Tom together working rate = Working rate of Sam + Working rate of Tom

Now, we want to calculate working rate of Sam alone.

So,  

Working rate of Tom = Sam and Tom together working rate - Working rate of Sam

1/x = 1/2 - 1/7

1/x = (7-2)/14

1/x = 5/14

x = 14/5

x = 2.8 hours or 2 hours + (0.8*60)minutes i.e. 2 hours 48 minutes

Time taken by Sam to finish the work alone is 2.8 hours or 2 hours 48 minutes.

Answer 2

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