Question

Wendy can wash a car twice as fast as Jason. When they work together, Wendy and Jason can wash a large van in 2 hours. How many hours would it take Jason to wash the van by himself?

Answer 1

i believe the answer is 6.

Answer 2

Jason will take 6 hours to was the car alone.

Solution-

Given that Wendy can wash a car twice as fast as Jason, i.e time taken by Jason is twice than that of Wendy for doing a same work.

Let us assume that,

Jason alone will take 2x hours, so Wendy alone will take x hours

So, the amount of work done by Jason in 1 hour is
`(1)/(2x)`

Likewise, the amount of work done by Wendy in 1 hour is
`(1)/(x)`

Net work done by both in one hours is,

`=(1)/(2x)+(1)/(x)=(3)/(2x)`

So, working together they will do
`(3)/(2x)`th of work in 1 hour.

Then, the total time taken by them for completing the task or doing 1 job,

`=(1)/((3)/(2x)) =(2x)/(3)\ hours`

But, given in the question that they take 2 hours to complete the job, so

`\Rightarrow (2x)/(3)=2`

`\Rightarrow x=3\ hours`

So, Wendy will take 3 hours to complete the task and Jason will take (3×2)=6 hours.