SOLUTION: Two water pipes together can fill a certain tank in 8.4 h. The smaller pipe alone takes 1.7 h longer than the larger pipe to fill that same tank. How long would it take the larger

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Question 1057931: Two water pipes together can fill a certain tank in 8.4 h. The smaller pipe alone takes 1.7 h longer than the larger pipe to fill that same tank. How long would it take the larger pipe alone to fill the tank? Keep three significant digits.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the individual rates is the rate for both pipes combined. The rate unit should be as TANKS%2FHOUR. 
PIPE                RATE
SMALL              1%2F%28x%2B1.7%29
LARGE              1%2Fx
BOTH TOGETHER      1%2F8.4

1%2F%28x%2B1.7%29%2B1%2Fx=1%2F8.4

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for the larger pipe
to fill the tank
+t+%2B+1.7+ = time in hrs for the smaller
pipe to fill the tank
------------------------
Add their rates of filling to get their
rate filling together
--------------------
rate for smaller pipe:
[ 1 tank filled ] / [ t + 1.7 hrs ]
rate for larger pipe:
[ 1 tank filled ] / [ t hrs ]
rate for both pipes together:
[ 1 tank filled ] / [ 8.4 hrs ]
-----------------------------
+1%2F%28+t+%2B+1.7+%29+%2B+1%2Ft+=+1%2F8.4+
Multiply both sides by +t%2A%28+t%2B1.7+%29%2A8.4+
+8.4t+%2B+8.4%2A%28+t+%2B+1.7+%29+=+t%2A%28+t+%2B+1.7+%29+
+8.4t+%2B+8.4t+%2B+14.28+=+t%5E2+%2B+1.7t+
+t%5E2+-+15.1t+-+14.28+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-15.1+
+c+=+-14.28+
This is some tough calculations. You can finish
and +t+ is time in hrs for larger pipe to fill tank
Check my math so far