Rates and ProportionDate: 7/11/96 at 8:10:9 From: Anonymous Subject: Rates and Proportion 10 men can build 2 boats in 4 days. Hom many men are needed to build 5 boats in 2 days? Date: 7/11/96 at 9:16:57 From: Doctor Patrick Subject: Re: Rates and Proportion First we need to figure out how long it takes a man to build a boat, and then we can apply that information to the question. If 10 men can build 2 boats in 4 days then the same 10 men should be able to build 1 boat in 2 days, since they would be building half as many boats in half as much time. Does this make sense? Then we can also say that if 10 men can build 1 boat in 2 days then 20 men should be able to build a boat in 1 day, since twice the number of men should be able to work twice as fast, right? This would also mean that 1 man would take 20 days to build 1 boat. Now we reverse the process and use this information to figure out how many men are needed to build 5 boats in two days. It would take one man 100 days to build five boats (20 days per boat*5 boats). If we want to cut this time down to 2 days we will need to increase the number of men by the same amount that we cut the time. Since the time is to be divided by 50 (100/50=2), we need to multiply the number of men by 50 also. Since 1 (the number of men who could build the boats in 100 days) times 50 = 50, it will take 50 men to build 5 boats in two days. -Doctor Patrick, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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