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)   (Show Source): You can put this solution on YOUR website!
.

Let d be the length of the road (the unknown value under the problem's question).


The rate of A is    of the road length per day;  rate of B is    of the road length per day.


Their combined rate working together is then   +  =  =  =   of the road per day.


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


In 15 days, A will build  ;  B will build  .


From the condition, we have this equation


     -  = 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          =  = 50*120 = 6000 meters.

Solved.



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