SOLUTION: NE PIPE CAN FILL A TANK IN 3 HOURS AND ANOTHER PIPE CAN FILL THE TANK IN 6 HOURS. HOW LONG WILL IT TAKE TO FILL THE TANK IF BOTH PIPES ARE USED AT THE SAME TIME?

Algebra ->  Equations -> SOLUTION: NE PIPE CAN FILL A TANK IN 3 HOURS AND ANOTHER PIPE CAN FILL THE TANK IN 6 HOURS. HOW LONG WILL IT TAKE TO FILL THE TANK IF BOTH PIPES ARE USED AT THE SAME TIME?      Log On


   

Question 1143159: NE PIPE CAN FILL A TANK IN 3 HOURS AND ANOTHER PIPE CAN FILL THE TANK IN 6 HOURS. HOW LONG WILL IT TAKE TO FILL THE TANK IF BOTH PIPES ARE USED AT THE SAME TIME?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of filling
Rate of 1st pipe:
[ 1 tank filled ] / [ 3 hrs ]
Rate of 2nd pipe:
[ 1 tank filled ] / [6 hrs ]
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Let +t+ = time in hrs to fill the tank
using both pipes
+1%2F3+%2B+1%2F6+=+1%2Ft+
Multiply both sides by +6t+
+2t+%2B+t+=+6+
+3t+=+6+
+t+=+2+
Using both pipes, it takes 2 hrs to fill tank
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check:
+2%2F6+%2B+1%2F6+=+1%2F2+
+3%2F6+=+1%2F2+
+1%2F2+=+1%2F2+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Traditional algebraic approach, using the fractions of the tank each pipe fills in an hour....

Let x be the number of hours it takes the two pipes together to fill the tank. Then 1/x is the fraction of the tank the two pipes fill in 1 hour.

Then since the two pipes take 3 and 6 hours to fill the tank alone, the fractions of the tank they fill in one hour are 1/3 and 1/6. So

1%2F3%2B1%2F6=1%2Fx

Solve using basic algebra....

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(2) A logical reasoning approach, using the least common multiple of the times the two pipes take individually to fill the tank....

The LCM of 3 hours and 6 hours is 6 hours. Consider what the two pipes could do in 6 hours.

The larger pipe, at 3 hours per tank, could fill the tank 2 times in 6 hours; the smaller pipe could fill the tank 1 time in 6 hours.

That means in 6 hours the two tanks together could fill the tank 3 times.

And that means together they could fill the tank 1 time in 6/3=2 hours.

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(3) Another logical reasoning approach that some students find easy to use....

The smaller pipe takes twice as long as the larger pipe to fill the tank. That means the smaller pipe is like half of the larger pipe. So when the two pipes are working together, it is like having 1.5 of the larger pipes.

And the amount of time it would take 1.5 of the larger pipes to fill the tank is 3/1.5 = 2 hours.