a particular pipe can fill a tank in 7 hours. when a second pipe is added, the tank can be filled in only 2 hours. how long would it take the second pipe to fill the tank by itself?
Make this chart, putting x for the hours required for the 2nd pipe alone,
since that's what we are to find:
number of hours rate in
tanks filled required tanks/hour
-----------------------------------------------------------------
1st pipe alone
2nd pipe alone x
both pipes together
Fill in 7 for the hours required for the first pipe alone.
Fill in 2 for the hours required for both pipes together.
number of hours rate in
tanks filled required tanks/hour
-----------------------------------------------------------------
1st pipe alone 7
2nd pipe alone x
both pipes together 2
In all cases exactly 1 tank was filled. Therefore we put 1 for the number
of tanks that were filled in all three cases:
number of hours rate in
tanks filled required tanks/hour
-----------------------------------------------------------------
1st pipe alone 1 7
2nd pipe alone 1 x
both pipes together 1 2
Fill in the three rates in tanks/hour by dividing the number of tanks
filled (1) by the hours required:
number of hours rate in
tanks filled required tanks/hour
-----------------------------------------------------------------
1st pipe alone 1 7 1/7
2nd pipe alone 1 x 1/x
both pipes together 1 2 1/2
The equation comes from
+ =
+ =
Solve that and get x = 2.8 hours or 2 hours 48 minutes.
Edwin