SOLUTION: A and B build a road. A alone needs 40 days. B alone needs 24 days. A and B start from the opposite ends and work to the middle. They met at a point that is 750 meters from the cen

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Question 1163838: A and B build a road. A alone needs 40 days. B alone needs 24 days. A and B start from the opposite ends and work to the middle. They met at a point that is 750 meters from the center point of the road. How long is the road?
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
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Let d be the length of the road (the unknown value under the problem's question).


The rate of A is  1%2F40  of the road length per day;  rate of B is  1%2F24  of the road length per day.


Their combined rate working together is then  1%2F40 + 1%2F24 = 3%2F120+%2B+5%2F120 = 8%2F120 = 1%2F15  of the road per day.


So, they complete their job in 15 days working together.


In 15 days, A will build  %2815%2F40%29%2Ad;  B will build  %2815%2F24%29%2Ad.


From the condition, we have this equation


    %2815%2F24%29d - %2815%2F40%29%2Ad = 2*750 = 1500  meters.


Multiply both sides by 120.  You will get then


    15*5d - 15*3d = 1500*120

    75d   - 45d   = 1500*120

    30d           = 1500*120

       d          = %281500%2A120%29%2F30 = 50*120 = 6000 meters.

Solved.