# SOLUTION: Bart can complete his science task twice as quickly as Carl can. When they Work together, the task takes 3 hours. How long would it take Carl to do the work alone?

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 Question 264387: Bart can complete his science task twice as quickly as Carl can. When they Work together, the task takes 3 hours. How long would it take Carl to do the work alone?Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!Bart can complete his science task twice as quickly as Carl can. When they Work together, the task takes 3 hours. How long would it take Carl to do the work alone? ``` Make this chart NUMBER OF TASKS RATE TIME Bart Carl Both together In all three cases, Bart alone, Carl alone, and both together, they will all do just 1 task so we put 1 for the NUMBER OF TASKS in each of the three cases NUMBER OF TASKS RATE TIME Bart 1 Carl 1 Both together 1 The question asks: ``` >>...How long would it take Carl to do the work alone?...<< ``` So we put x for Carl's time: NUMBER OF TASKS RATE TIME Bart 1 Carl 1 x Both together 1 ``` >>...Bart can complete his science task twice as quickly as Carl can...<< ``` That means Bart requires only HALF as much time, so we divide Carl's by 2 to get Bart's time. So we put x/2 for Bart's time. NUMBER OF TASKS RATE TIME Bart 1 x/2 Carl 1 x Both together 1 ``` >>...When they work together, the task takes 3 hours...<< ``` So we put 3 for the time for "both together"": NUMBER OF TASKS RATE TIME Bart 1 x/2 Carl 1 x Both together 1 3 Now we figure the three rates in tasks per hour. Bart's rate = Carl's rate = "Both together" rate = So fill those in: NUMBER OF TASKS RATE TIME Bart 1 2/x x/2 Carl 1 1/x x Both together 1 1/3 3 Now we get the equation from the rates: Bart's RATE + Carl's RATE = the RATE for "both together": Get a common denominator of and multiply every term by So it would take Carl 9 hours to complete the task. Edwin```