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

Answer-

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 $\dfrac{1}{2x}$

Likewise, the amount of work done by Wendy in 1 hour is $\dfrac{1}{x}$

Net work done by both in one hours is,

$=\dfrac{1}{2x}+\dfrac{1}{x}=\dfrac{3}{2x}$

So, working together they will do $\dfrac{3}{2x}$th of work in 1 hour.

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

$=\dfrac{1}{\frac{3}{2x}} =\dfrac{2x}{3}\ hours$

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

$\Rightarrow \dfrac{2x}{3}=2$

$\Rightarrow x=3\ hours$

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