Question 1163838
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<pre>

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


The rate of A is  {{{1/40}}}  of the road length per day;  rate of B is  {{{1/24}}}  of the road length per day.


Their combined rate working together is then  {{{1/40}}} + {{{1/24}}} = {{{3/120 + 5/120}}} = {{{8/120}}} = {{{1/15}}}  of the road per day.


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


In 15 days, A will build  {{{(15/40)*d}}};  B will build  {{{(15/24)*d}}}.


From the condition, we have this equation


    {{{(15/24)d}}} - {{{(15/40)*d}}} = 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          = {{{(1500*120)/30}}} = 50*120 = 6000 meters.
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Solved.