Tom and huck start a business painting fences. They paint aunt polly's fence and find that they can paint a 200 ft squared fence in 40 min if they worked together. If huck works 4 times faster than tom, how long would it take each of them to paint a 500 ft squared fence working alone?
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huck's rate is 4 times that of tom so if you put tom's rate as r, hucks rate is 4r
together they can paint 200 ft in 40 minutes so their combined rate is 200/40 = 5 square feet per minute. so
r + 4r = 5
so tom can paint 1 square foot per minute and huck can paint 4 square feet.
tom therefore takes 500 minutes to paint the fence and huck takes 125.
welcome. it occurs to me that there may be a snappier way to do this but i don't know it.