Working together, Tom and Jon can clean a car in 5.14 hours. Had Tom done it alone it would take him 22 hours. How long would it take Jon to clean alone?

Question

Working together, Tom and Jon can clean a car in 5.14 hours. Had Tom done it alone it would take him 22 hours. How long would it take Jon to clean alone?

Answer 1

Let T be the amount of time it takes Tom to clean the car and J the amount of time it takes Jon to clean it. 

 

We now come up with an expression based on the problem

 

T_t + T_j  = 22

 

T_j = 22 - 5.14

 

= 16.86 hrs

 

That's the amount of time it would take John to clean the car alone. Hope I was helpful. 

 

Mayuran

Answer 2

Tom would take 22 hours to clean the car alone,

This means Tom does 1/22 of the car per hour

 

Together they take 5.14 hours so we take

the part per hour of Tom, (1/22), added to the

part per hour of Jon (1/x) and multiply by the

5.14 hours and we get 100% of the job or 1

 

5.14(1/22 + 1/x) = 1

1/22 + 1/x = 1/5.14

1/x = 1/5.14 - 1/22

1/x = (22-5.14)/(113.08)

1/x = 16.86/113.08

16.86x = 113.08

x = 113.08/16.86

x = 6.71

 

It would take Jon 6.71 hours to do the car alone.

 

Does this make sense?  First off, we know the answer must

be more than 5.14 hours because alone either one will be

slower than they are together.  Yes.

Noting that Tom takes 22 hours alone, but together they

only take 5.14 hours we expect Jon to be a lot quicker than

Tom since the overall time is much less than half of Tom's

time alone.  Yes, 6.71 hours makes sense logically.