SOLUTION: Terry the frog and Charles the rabbit want to create a new math course consisting of 30 lessons. If they do the job together, it would take them 300 hours to finish the job. If the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Terry the frog and Charles the rabbit want to create a new math course consisting of 30 lessons. If they do the job together, it would take them 300 hours to finish the job. If the      Log On


   

Question 935391: Terry the frog and Charles the rabbit want to create a new math course consisting of 30 lessons. If they do the job together, it would take them 300 hours to finish the job. If they do the job separately, Terry would be 60 hours faster than Charles. When they do the job together, how many lessons should Terry expect to do?
Found 2 solutions by josmiceli, brysca:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What is true ( but not exactly stated ) is that each
one works at a certain rate which doesn't change.
------------------------
You can call +30+ lessons +1+ job since they
are not finished until they have +30+ lessons
------------------------
Let Charles rate of working be:
( 1 job ) / ( t hours ) = +1%2Ft+
----------------------------
Terry's rate of working is:
( 1 job ) / ( t - 60 hrs ) = +1+%2F+%28+t-60+%29+
since shorter time means faster
-----------------------------
If I add their rates of working, I get their
rate working together
+1%2Ft+%2B+1%2F%28+t-60+%29+=+1%2F300+
Multiply both sides by +300t%2A%28+t-60+%29+
+300%2A%28+t-60+%29+%2B+300t+=+t%2A%28+t-60+%29+
+300t+-+18000+%2B+300t+=+t%5E2+-+60t+
+t%5E2+-+660t+%2B+18000+=+0+
Use the quadratic formula
+t+=+%28+-%28-660%29+%2B-+sqrt%28+%28-660%29%5E2+-+4%2A1%2A18000+%29%29+%2F+%282%2A1%29+
+t+=+%28+660+%2B-+sqrt%28+435600+-+72000+%29%29+%2F+2+
+t+=+%28+660+%2B-+sqrt%28+363600+%29%29+%2F+2+
+t+=+%28+660+%2B+603+%29+%2F+2+
+t+=+1263%2F2+
+t+=+631.5+
+t+-+60+=+571.5+
--------------------
check:
+1%2Ft+%2B+1%2F%28+t-60+%29+=+1%2F300+
+1%2F631.5+%2B+1%2F571.5+=+1%2F300+
+.0015835+%2B+.0017497+=+.0033333+
+.0033332+=+.0033333+
( error due to rounding off )
--------------------------
If +x+ = the fraction of the job
done by Charles, then:
+x+ = ( his rate ) x ( time to finish )
+x+=+300+%2F+631.5+
+x+=+.47506+
and
+.47506%2A30+=+14.25+
Charles could finish 14 lessons, so
Terry could finish +30+-+14+, or
16 lessons
Hope I got this right






Answer by brysca(112) About Me  (Show Source):
You can put this solution on YOUR website!
step by step solution posted below
.
hope this helps!