Question 795806: 1.) A set of triplets, Darren, Derrick, and Daniel each alternate mowing the lawn, raking the leaves, and sweeping the driveway and walkway. If Derrick takes 6 hours to do all of the chores himself, while Darren does all of the chores in half the time as Derrick, and Daniel takes 1 hour longer than Darren, how long will it take the triplets to do all of the chores working together? a.) Translate into a work equation b.) write the equation without fractions. Solve the equation.
I figured out that Darren would take 3 hours on the task, Derrick 6, and Daniel 4. Then to figure out a work equation I did 1/3t+1/6t+1/4t(t), but now I am stuck. I am not even sure if I am on the right track so if you could help me that would be great. Thanks so much
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Derrick contributes 1/6 of an hour in an hour
Darren does all the chores in half the time as Derrick means Darren contributes 1/3 of an hour in an hour since he does all chores in 6/2 hours
Daniel takes 3 +1 hours to do chores and contributes 1/4 of an hour in an hour
therefore we have
1/6 +1/3 +1/4 = 1/t
2/12 +4/12 +3/12 = 1/t
9/12 = 1/t
t = 12/9 = 4/3
t = 1 hour and 20 minutes
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