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

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) (Show Source): You can put this solution on YOUR website!
Let = time in hrs for the larger unit
= time in hrs for the smaller unit
--------------------------------------------------
Add their rates of melting to get their rate melting together

Multiply both sides by

( can't use negative result )
and

---------------------
Larger unit takes 20 hrs
Smaller unit takes 60 hrs
------------------------------
check:

OK

Answer by VFBundy(438) (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:

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.
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