If Rachel were to paint her living room alone it would take five hours her sister Barbara could do the job in eight hours how many hours would it take them working together express your answer as a fraction reduced to lowest terms if needed

40/13 hours

Step-by-step explanation:

Let 1 represent the room being painted.

1/5 would represent 1/5 of a room painted in 1 hour.

1/8 would represent 1/8 of a room being painted in 1 hour

But they are are working together so

(1/5) x + (1/8) x = 1

The lowest common denominator is 5 * 8 = 40

[ (1/5) x * 40 + (1/8) x * 40] = 1

8x + 5x = 40

13x = 40

x = 40/13

x = 3.077 hours

But you want a fraction as your answer so it is 3 1/13 or 40/13

You should notice that 3.077 is smaller than the lowest amount of time both of them use. That always happens with these questions.