SOLUTION: Michelle can type a 20 page paper in 5 hours. Amanda can type a 60 page paper in 8 hours. Working together, how long would it take them to complete a 40 page paper?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Michelle can type a 20 page paper in 5 hours. Amanda can type a 60 page paper in 8 hours. Working together, how long would it take them to complete a 40 page paper?      Log On


   

Question 878144: Michelle can type a 20 page paper in 5 hours. Amanda
can type a 60 page paper in 8 hours. Working
together, how long would it take them to complete a
40 page paper?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You can define a +20+ page letter as +1+ job
A +60+ page letter would then be +60%2F20+=+3+ jobs
A +40+ page letter would then be +40%2F20+=+2+ jobs
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Michelle's rate of typing is ( 1 job ) / ( 5 hrs )
Amanda's rate of typing is ( 3 jobs ) / ( 8 hrs )
Typing together, their rate is ( 2 jobs ) / ( t hrs )
-----------------
Add their rates of typing to get their rate typing together
+1%2F5+%2B+3%2F8+=+2%2Ft+
Multiply both sides by +40t+
+8t+%2B+15t+=+80+
+23t+=+80+
+t+=+3+%2B+11%2F80+ hrs
Convert +11%2F80+ to minutes
+%2811%2F80+%29%2A60+=+33%2F4+ min approximately
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Together, they can type a 40 page letter in 3 hrs 8 min
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check:
+1%2F5+%2B+3%2F8+=+2%2Ft+
+1%2F5+%2B+3%2F8+=+2%2F%28+80%2F23+%29+
+1%2F5+%2B+3%2F8+=+46%2F80+
+8%2F40+%2B+15%2F40+=+23%2F40+
+23%2F40+=+23%2F40+
OK