SOLUTION: A small heating unit takes 56 h longer to melt a piece of iron than does a larger unit. Working together, the heating units can melt the iron in 21 h. How long would it take each h

Click here to see ALL problems on Equations

Question 1058316: A small heating unit takes 56 h longer to melt a piece of iron than does a larger unit. Working together, the heating units can melt the iron in 21 h. How long would it take each heating unit, working alone, to melt the iron?
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Rate of heating for large unit alone:
[ 1 piece of iron melted ] / [ t hrs ]
Rate of heating for small unit alone:
[ 1 piece of iron melted ] / [ t + 56 hrs ]
Rate for both units together:
[ 1 piece of iron melted ] / [ 21 hrs ]
--------------------------------------
Add the different units rates of melting
to get rate working together:

Multiply both sides by

I'll complete square:

and

------------------
The smaller unit alone takes 84 hrs
The larger unit alone takes 28 hrs
---------------------------------
check:

OK