SOLUTION: Maria can do a certain task in 30 minutes. Dana can accomplish that same task in 20 minuets. One day Maria stated the task, then after 10 minutes she was joined by Dana and they fi

Question 1198746: Maria can do a certain task in 30 minutes. Dana can accomplish that same task in 20 minuets. One day Maria stated the task, then after 10 minutes she was joined by Dana and they finished the task together. How long did it take them to finish the task once the stated working together ?
Found 3 solutions by josgarithmetic, greenestamps, math_tutor2020:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
So much like many of the other examples of this type
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

First find how long it would take the two of them together to do the whole job. Note I prefer a non-standard method for doing that....

The least common multiple of the two given times is 60 minutes. In 60 minutes Maria can do the task 60/30 = 2 times; Dana can do it 60/20 = 3 times. So in 60 minutes the two together could do the task 5 times; and that means the two together can do the single task in 60/5 = 12 minutes.

In this problem, Maria works for 10 minutes before Dana joins her. In that time, the fraction of the job that Maria does is 10/30 = 1/3.

So 2/3 of the job remains to be done when they start working together. Since it takes them 12 minutes to do the whole job together, it takes them (2/3)*12 = 8 minutes to finish.

ANSWER: 8 minutes to finish the job together

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

The LCM of 30 and 20 is 60.

Let's say the task is moving 60 boxes.

Maria can move 60 boxes in 30 minutes.
Her rate is 60/30 = 2 boxes per minute.
rate = (amount done)/(time)
This is if Maria works alone.

Dana, when working alone, can do the same job in 20 minutes.
rate = (amount done)/(time)
rate = (60 boxes)/(20 min)
rate = 3 boxes per min

Given information: "One day Maria stated the task, then after 10 minutes she was joined by Dana".

If Maria works for 10 minutes, and her rate is 2 boxes per minute, then she has moved 2*10 = 20 boxes in that timespan.
amount done = (rate)*(time)

There are 60-20 = 40 boxes left to be moved.
The two women's individual rates add to 2+3 = 5 boxes per minute.
This assumes they work efficiently without getting in each others' way.

If their task is to move 40 boxes, and their combined rate is 5 boxes per min, then:
(rate)*(time) = amount done
time = (amount done)/(rate)
time = (40 boxes)/(5 boxes per min)
time = 8 minutes is the final answer.
This is the amount of time they work together to finish up the task (moving the remaining 40 boxes).

The 60 I chose at the very start of the problem isn't special at all.
You can replace it with any other positive integer you wanted and still get the same final answer.
I chose 60 so that the divisions resulted in whole numbers.

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