SOLUTION: BJ can overhaul a boat's diesel inboard engine in 20 hours. His apprentice takes 6 hours to do the same job. how long would it take them working together assuming no gain or loss i

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Question 1025945: BJ can overhaul a boat's diesel inboard engine in 20 hours. His apprentice takes 6 hours to do the same job. how long would it take them working together assuming no gain or loss in efficiency
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, you have to imagine 2 people working
on an engine without getting in eachother's way.
It's not like painting a fence.
But as long as you can assume that, add their
rates of working to get their rate working together.
BJ's rate:
[ 1 engine overhauled ] / [ 20 hrs ]
Apprentice's rate:
[ 1 engine overhauled ] / [ 6 hrs ]
Let +t+ = their time in hrs working together
to overhaul engine
Rate working together:
[ 1 engine overhauled ] / [ t hrs ]
------------------------------
+1%2F20+%2B+1%2F6+=+1%2Ft+
Multiply both sides by +60t+
+3t+%2B+10t+=+60+
+13t+=+60+
+t+=+4+%2B+8%2F60+
Working together, it takes them 4 hrs and 8 min
check:
+1%2F20+%2B+1%2F6+=+1%2Ft+
+1%2F20+%2B+1%2F6+=+1%2F%2860%2F13%29+
+1%2F20+%2B+1%2F6+=+13%2F60+
+3%2F60+%2B+10%2F60+=+13%2F60+
+13%2F60+=+13%2F60+
OK