## 14 POINTS! Problem: As a punishment for something naughty that we did, my little brother and I have to whitewash both sides of a

Question

14 POINTS!
Problem:
As a punishment for something naughty that we did, my little brother and I have to whitewash both sides of a fence. We start at the same time, and we each work at a constant rate.

If we each whitewash one side, I’ll finish in 2 hours and my brother will finish in 3 hours. But I’m a nice kid, so after I finish my side, I go around to the other side and help my brother finish his side. From the time I start helping him, how many minutes does it take us to finish the job?
Hint(s):
Indeed, my brother would have an hour to go if I didn’t help him. But I’m faster than he is! So when I help him, we should finish in less than half the time it would take for him to do the job alone.
What fraction of a side can I paint in an hour? How about my brother? How about both of us together?

0

1. What fraction of side per hour

you
= 1 side / 2 hrs
= 1/2 side/hr

brother
= 1 side / 3 hrs
= 1/3 side/hr

combined rate
= 1/3 + 1/2
= (1/3)(2/2) + (1/2)(3/3)
= 2/6 + 3/6
= 5/6 side/hr

after 2 hrs you are done with your side, brother has 2*(1/3) = 2/3 done.
3/3 – 2/3 = 1/3 left to paint

(1/3 side)*(6 hr / 5 side) = 2/5 hr
2/5 hr * 60 min/hr = 24 min

2. 180 minutes to finish