Question

Sara can paint a small deck in 7 hours. Together with Joe, they can paint the deck in 3 hours.

How long would it take Joe to paint the deck by himself? Write a Rational Equation and use it to
solve for the answer to this question.

Answer 1

12/5 hours

Explanation:

Let the total area to be painted be X

Let S be the rate at which Sally paints and J be the rate at which Joe paints

We have:
X/S = 4 hours (1)

X/J = 6 hours (2)

(1) ÷ (2) ==>
LHS = X/S ÷ X/j = X/S × J/X ==> J/S (3)
RHS = 4/6 = 2/3 (4)

From (3) and (4)
J/S = 2/3 or J =2/3 × S

If they both paint at the same time time taken is

X/(S+J)
S + J = S + 2/3 *S = 5/3S
So time taken for both of them to paint is X/(5/3)*S = X/S * 3/5
But we know from (1) that X/S = 4 so time taken = 4 * 3/5 = 12/5 hours