Question 1097760
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Let D be the distance between the cities A and B.


Till the moment of the meeting the car A covered the distance (D + 30) km,
while the truck covered the distance of (D - 30) km. 


Car   A spent {{{(D+30)/50}}} hours to cover the distance (D+30) at the rate 50 km/h.

Truck B spent {{{(D-30)/40}}} hours to cover the distance (D-30) at the rate 40 km/h.


The time spent is the same, which gives you an equation

{{{(D+30)/50}}} = {{{(D-30)/40}}}.


To solve it, cross multiply and simplify:

40*(D+30) = 50*(D-30)  ====>

40D + 1200 = 50D - 1500  ====>  1200 + 1500 = 50D - 40D  ====>  10D = 2700  ====>  D = {{{2700/10}}}  = 270.


<U>Answer</U>.  The distance between the cities A and B is 270 kilometers.


<U>Check</U>.   {{{(270+30)/50}}} = 6 = {{{(270-30)/40}}}.   ! Correct !
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