SOLUTION: A small heating unit takes 40 h longer to melt a piece of iron than does a larger unit. Working together, the heating units can melt the iron in 15 h. How long would it take each h

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A small heating unit takes 40 h longer to melt a piece of iron than does a larger unit. Working together, the heating units can melt the iron in 15 h. How long would it take each h      Log On


   

Question 1137144: A small heating unit takes 40 h longer to melt a piece of iron than does a larger unit. Working together, the heating units can melt the iron in 15 h. How long would it take each heating unit, working alone, to melt the iron?
Found 2 solutions by josmiceli, VFBundy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for the larger unit
+t+%2B+40+ = time in hrs for the smaller unit
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Add their rates of melting to get their rate melting together
+1%2Ft+%2B+1%2F%28+t+%2B+40+%29+=+1%2F15+
Multiply both sides by +t%2A%28+t+%2B+40+%29%2A15+
+15%2A%28+t+%2B+40+%29+%2B+15t+=+t%2A%28+t++%2B+40+%29+
+15t+%2B+600+%2B+15t+=+t%5E2+%2B+40t+
+t%5E2+%2B+10t+-+600+=+0+
+%28+t+%2B+30+%29%2A%28+t+-+20+%29+
+t+=+20+ ( can't use negative result )
and
+t+%2B+40+=+60+
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Larger unit takes 20 hrs
Smaller unit takes 60 hrs
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check:
+1%2F20+%2B+1%2F60+=+1%2F15+
+.05+%2B+.01667+=+.06667+
+.06667+=+.06667+
OK

Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Rate larger unit takes to melt iron: 1/x per hour
Rate smaller unit takes to melt iron: 1/(x+40) per hour

Rate of both working together: 1/x + 1/(x+40) = 1/15 per hour

Solve for x:

1%2Fx+%2B+1%2F%28x%2B40%29+=+1%2F15

%28x%2B40%29%2Fx%28x%2B40%29+%2B+x%2Fx%28x%2B40%29+=+1%2F15

%28%28x%2B40%29%2Bx%29%2Fx%28x%2B40%29+=+1%2F15

%282x%2B40%29%2Fx%28x%2B40%29+=+1%2F15

15%282x%2B40%29+=+x%28x%2B40%29

30x+%2B+600+=+x%5E2+%2B40x

x%5E2+%2B+10x+-+600+=+0

%28x-20%29%28x%2B30%29+=+0

x = 20 and x = -30

Since the rate cannot be a negative number, we can ignore x = -30. So, the final answer is x = 20.

Rate larger unit takes to melt iron: 1/x per hour = 1/20 per hour
Rate smaller unit takes to melt iron: 1/(x+40) per hour = 1/60 per hour

So, working alone, the larger unit takes 20 hours to melt the iron and the smaller unit takes 60 hours.