Problem Solving

Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 8 hours. How long would it take Taimour to paint the fence alone?

(A) 6 hours
(B) 8 hours
(C) 14 hours
(D) 24 hours
(E) 32 hours

The OA is D.

What are the equations that I should use to solve this PS question? Could anyone give me some help? Please.

M7MBA wrote:Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 8 hours. How long would it take Taimour to paint the fence alone?

(A) 6 hours
(B) 8 hours
(C) 14 hours
(D) 24 hours
(E) 32 hours

We can PLUG IN THE ANSWERS, which represent Taimour's time alone.
Since Jamshid and Taimour working together takes 8 hours to paint the fence, Taimour's time alone must be more than 8 hours.
Eliminate A and B.
When the correct answer is plugged in, Jamshid's time alone will be 50% less than Taimour's time alone.
In other words, Jamshid's time alone will be 1/2 Tamour's time alone.

D: Taimour's time alone = 24 hours
Let the fence = 24 units.
Since Taimour alone takes 24 hours to paint the 24-unit fence, Taimour's rate = w/t = 24/24 = 1 unit per hour.
Since Jamshid and Taimour together take 8 hours to paint the 24-unit fence, their combined rate = w/t = 24/8 = 3 units per hour.
Jamshid's rate = (combined rate for Jamshid and Taimour) - (Taimour's rate alone) = 3-1 = 2 units per hour.
Since Jamshid's rate = 2 units per hour, Jamshid's time alone to produce the 24-unit fence = w/r = 24/2 = 12 hours.
Success!
Jamshid's time alone (12 hours) is 1/2 Taimour's time alone (24 hours).

The correct answer is D.

Let total work be 'w' and number of hours taken taimur is 'x', so hours taken by Jamshid is 'x/2'
Now,
work done by Taimur per hour= w/x
work done by Jamshid per hour= 2w/x

Now, when Taimur and Jamshid work together they finish it in 8 hours, work done per hour by both combined= w/8

So, w/x +2w/x= w/8

On solving,
we get x= 24