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

Answers ( No )

    0
    2021-11-25T19:05:07+00:00

    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

    0
    2021-11-25T19:05:16+00:00

    180 minutes to finish

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