SOLUTION: I swear I have a mental blockage when it comes to maths. This appeared in a story book i was reading to my boy and could not answer i. If a bath takes 5 minutes to fill and 8 mi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I swear I have a mental blockage when it comes to maths. This appeared in a story book i was reading to my boy and could not answer i. If a bath takes 5 minutes to fill and 8 mi      Log On


   

Question 712571: I swear I have a mental blockage when it comes to maths. This appeared in a story book i was reading to my boy and could not answer i.
If a bath takes 5 minutes to fill and 8 minutes to empty: how long does it take to fill?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If a bath takes 5 minutes to fill and 8 minutes to empty: how long does it take to fill when the faucet is running and the drain is open?
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faucet rate = 1/5 job/min
drain rate = 1/8 job/min
Together rate = 1/x job/min
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Equation:
rate - rate = together rate
1/5 - 1/8 = 1/x
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Multiply thru by 40x to get:
8x - 5x = 40
3x = 40
x = 40/3 = 13 1/3 minutes (time to fill the tub)
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Don't feel bad. Most people have no idea how to
work these rate problems.
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let # of minutes to fill be m:
If a bath takes 5min to fill and 8min to empty, then we have
m%2F5+-+m%2F8+=+1
%288m-+5m%29%2F%285%2A8%29+=+1
8m-+5m+=+1%285%2A8%29
3m+=+1%2A40
3m+=+40
m+=+40%2F3
m+=+13.33
Answer: 13.33 minutes

or, if you want in hours:
let # of hours to fill be h:
If a bath takes 5min=%285%2F60%29h=0.0833h to fill and 8min=0.133h to empty
h%2F%280.0833%29+-+h%2F%280.133%29+=+1
%280.133h-+0.0833h%29%2F%280.133%2A0.0833%29+=+1
0.0497h+=+1%2A%280.133%2A0.0833%29
0.0497h+=+0.0110789
h+=+0.0110789%2F0.0497
h+=+0.223

Answer: 0.223 hours