Question

. It takes Sarah 6 hrs longer to paint a room

than it takes John. Working together, they
can paint the room in 4 hours. How long in
hours) would it take Sarah to paint the room
alone?

Answer 1

It took 12 hours for Sarah to paint the room alone.

Explanation:

Step 1 :

Let,

John's total time = x hours

Sarah's total time = (x + 6) hours

Working together = 4 hours

Step 2 :

• In one hour John can paint 1/x of the house.
• In one hour Sarah can paint 1/(x+6) of the house.
• In one hour, they both can paint 1/4 of the house.

Step 3 :

⇒ 1/x + 1/(x+6) = 1/4

⇒ (x+6) + x / x(x+6) = 1/4

⇒ 4 (2x+6) = x(x+6)

⇒ 8x + 24 = x^2 + 6x

⇒ x^2 -2x -24 = 0

Step 4 :

The roots of the equation x^2 -2x -24 = 0 are x=6 and x=-4

Since time cannot be negative, Consider x= 6.

∴ Time taken by john = 6 hours.

Step 5 :

Time taken by Sarah = (x + 6) hours = 6+6 = 12 hours