SOLUTION: two pipes working together, can fill a tank in 20 minutes. working alone. the smaller pipe takes 42 minutes longer than the larger pipe to fill the tank. how long would it take the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: two pipes working together, can fill a tank in 20 minutes. working alone. the smaller pipe takes 42 minutes longer than the larger pipe to fill the tank. how long would it take the      Log On


   

Question 968465: two pipes working together, can fill a tank in 20 minutes. working alone. the smaller pipe takes 42 minutes longer than the larger pipe to fill the tank. how long would it take the smaller pipe alone to fill the tank?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in minutes for the larger
pipe to fill the tank
+t+%2B+42+ = time in minutes for the smaller pipe
to fill the tank
------------------
Add their rates to get rate working together
Working together:
[ 1 pipe filled ] / [ 20 min ]
+1%2F+t+%2B+1%2F%28+t%2B42+%29+=+1%2F20+
Multiply both sides by +t%2A%28+t%2B42+%29%2A20+
+20%2A%28+t%2B42+%29+%2B+20t+=+t%2A%28+t%2B42+%29+
+20t+%2B+840+%2B+20t+=+t%5E2+%2B+42t+
+t%5E2+%2B+2t+-+840+=+0+
Use quadratic formula
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+2+
+c+=+-840+
+t+=+%28+-2+%2B-+sqrt%28+2%5E2+-+4%2A1%2A%28-840%29+%29%29+%2F+%282%2A1%29+
+t+=+%28+-2+%2B-+sqrt%28+4+%2B+3360+%29%29+%2F+2+
+t+=+%28+-2+%2B-+sqrt%28+3364+%29+%29+%2F+2+
+t+=+%28+-2+%2B+58+%29+%2F+2+
+t+=+56%2F2+
+t+=+28+
and
+t+%2B+42+=+70+
The smaller pipe takes 70 min to fill the tank
-------------------
check:
+1%2F+t+%2B+1%2F%28+t%2B42+%29+=+1%2F20+
+1%2F+28+%2B+1%2F70+=+1%2F20+
+.035714+%2B+.014286+=+.05+
+.05+=+.05+
OK