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Question 472712: i need your help.. please solve this problem:
June can finish an accounting work in 8 hours . While Leo can do the same job in 6 hours. After 2 hours of working together, June left Leo for lunch and Leo finished the job. FIND THE AMOUNT OF TIME FOR LEO TO FINISH THE JOB..
thanks so much! ^^
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = number of units of work
that's the formula to solve this type of problem.
june can finish the job in 8 hours working alone.
leo can do the same ob in 6 hours working alone.
june's rate of work is equal to 1/8 of the job per hour.
leo's rate of work is equal to 1/6 of the job per hour.
they worked on the job for 2 hours working together.
their combined rate is additive.
the combine rate is 1/8 + 1/6 which is equal to 6/48 + 8/48 = 14/48 of the job per hour.
working together, the formula becomes:
rate * time = number of units of work.
14/48 * 2 = number of units of work.
number of units of work = 28/48 of the job.
now june leaves and leo is left to finish the job alone.
the amount of the job left to be completed is 1 - 28/48 which is equal to 48/48 - 28/48 which is equal to 20/48 of the job.
leo's rate of work is 1/6 of the job per hour.
rate * time = number of units of work is the formula you use again.
this time, though, the figures used are:
1/6 * T = 20/48
T is the amount of time in hours.
Solve for T to get:
T = (20/48) / (1/6) which is equal to 20/48 * 6 which is equal to 120/48 which is equal to 2.5 hours which is equal to 2 hours and 30 minutes.
they worked together for 2 hours and leo finished the job in an additional 2 and 1/2 hours for a total of 4 and 1/2 hours.
let's see if this is right.
back to the formula:
rate * time = number of units of work.
their combined rate was 1/6 + 1/8 = 14/48 of the job per hour.
they worked together for 2 hours to complete 28/48 of the job.
leo's rate was 1/6 of the job per hour.
he worked for 2.5 hours to complete 1/6 * 2.5 = 5/12 of the job.
5/12 is equivalent to 20/48.
28/48 and 20/48 is equal to 48/48 which is equal to 1 which is the total number of units that needed to be produced, so the job is done.
leo took 2 hours and a half to finish the job.
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