Distance = rate x height

Question

Jason can clean a tank in 6 hours. Jason and Lucy can clean it in 3.5 hours. How long does it take Lucy alone?

Answer 1

Let X = how many hours it takes Lucy to clean the tank

 

Lucy can clean the tank in X hours  ==>  in 1 hour Lucy can clean 1/X of the tank

 

Jason can clean a tank in 6 hours  ==>  in 1 hour Jason can clean 1/6 of a tank

 

Jason and Lucy clean it in 3.5 hours  ==> in 1 hour Jason and Lucy can clean 1/3.5 of a tank

 

The sum of the amount they can clean individually in 1 hour must be the same as the amount they can clean together in 1 hour, so 

 

1/X + 1/6 = 1/3.5

 

Combine the left hand side over a common denominator

 

(6+X)/(6X) = 1/3.5

 

Cross multiply

 

6X = (6+X)*3.5

6X = 21 + 3.5X

2.5X = 21

X = 21/2.5 = 8.4 hours

 

It would take Lucy 8.4 hours to clean the tank alone 

 

Answer 2

Mattie,

 

What would happen if they were to clean 2 tank? They would take 7 hours, right? 6 hours coming form Jason and 1 hour coming from Lucy (3.5(2)=7=6+1). Do you see that the question has already been answered? Ans. 1 hour. I hope this helps.