SOLUTION: Marie can eat a cake in 10 minutes. Anne joins her after 3 minutes. Together they eat the rest of the cake in 4 minutes. How long would it take Anne to eat the cake alone?

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Question 94604: Marie can eat a cake in 10 minutes. Anne joins her after 3 minutes. Together they eat the rest of the cake in 4 minutes. How long would it take Anne to eat the cake alone?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Marie can eat a cake in 10 minutes. Anne joins her after 3 minutes. Together they eat the rest of the cake in 4 minutes. How long would it take Anne to eat the cake alone?
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Marie DATA:
Time = 10 minutes/job ; Rate = 1/10 job/min
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Anne DATA:
Time = x minutes/job ; Rate = 1/x job/min
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EQUATION:
Anne joins her after 3 minutes and together they eat the rest of the
cake in 4 minutes.
In 3 minutes Marie will have completed (3/10)ths of the job.
They then eat the remaining (7/10)th together in 4 minutes.
(4minutes)[(1/10)+(1/x)](job/minute) = 7/10 job
4[[(x+10)/10x] = 7/10
4(x+10)/x) = 7
4(x+10) = 7x
3x=40
x= 13 1/3 minutes (Anne's time alone to do the job)
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Cheers,
Stan H.