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Question 665596: Tom, Dick, and Harry begin working together to dig a trench. Tom works twice as fast as Dick and one-third as fast as Harry. After one hour of work, Tom is called away. After Tom leaves, the other two finish the job in three hours. How long would it have taken Harry to dig the trench alone?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Tom, Dick, and Harry begin working together to dig a trench.
Tom works twice as fast as Dick and one-third as fast as Harry.
After one hour of work, Tom is called away.
After Tom leaves, the other two finish the job in three hours.
How long would it have taken Harry to dig the trench alone?
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Let t, d, h = time required by each man to dig the trench alone
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Will try to get them all in terms of d
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"Tom works twice as fast as Dick"
t =  d, (Tom required half the time of Dick to do the job)
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"tom is one-third as fast as Harry."
t = 3h, (Tom requires 3 times the time of Harry)
Replace t with (1/2)d
d = 3h
Divide both sides by 3
h =  d, (Harry requires only 1/6 the time of Dick)
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Let the completed job = 1
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A shared work equation (Tom worked 1 hr, the others worked 4 hrs)
 +  +  = 1
Multiply by 6d, to clear the denominators, results
12 + 6(4) + 36(4) = 6d
12 + 24 + 144 = 6d
d = 
d = 30 hrs, time required by Dick working alone
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" How long would it have taken Harry to dig the trench alone?"
h = *30
h = 5 hrs Harry working alone
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Just hire Harry, send the others home
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:
Check this
 +  +  =
.0667 + .1333 + .8 ~ 1, confirms our solution
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