Question

It takes Ralph 12 hours to paint a fence alone. Lisa can do the same job in 15 hours. If Ralph paints alone for 40 minutes before Lisa begins helping, how long must they work together to finish painting the fence? Give your answer as a simplified fraction.

Answer 1

After 40 minutes, Ralph has already painted (40/60)/12=1/18 of the fence

Lisa's speed is 1/15 fence/hour, Ralph's speed is 1/12 fence/hour, hence when they help each other their combined speed is 1/15+1/12=3/20

Thus we need to solve 3/20*x=17/18 thus x=170/27 hours (approx 6 hours 15 mins)