Question 1061532
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Nora leaves Town A and walks towards Town B at a speed of 100 m/min. At the same time , Kate and Lixin walk from Town B towards 
Town A at a speed of 80 m/min and 75 m/min respectively. If Nora meets Lixin 6 minutes after passing Kate, 
find the distance between Town A and Town B.
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Let L be the distance between the cities and let "t" be the time (in minutes) from the start to the moment Nora meets Kate.

The first equation is 

100*t + 80*t = L              (1)   (Nora's walked distance + Kate's distance = L at the moment they meet each other)


Also, the time from the start to the moment Nora meets Lixin is (t+6) minutes.

And the second equation is similar to the first one:

100*(t+6) + 75*(t+6) = L.     (2)   (Nora's walking distance + Lixin's distance = L at the moment they meet each other)


Equations (1) and (2) have equal right sides.
Hence, their left sides are equal, too:

100*t + 80*t = 100*(t+6) + 75*(t+6).


It is a single equation for one unknown "t". Simplify and solve for "t":

180*t = 175t + 600 + 450,

180t - 175t = 1050,

5t = 1050,

t = {{{1050/5}}} = 210.


Thus we found the time "t" till the first meeting. It is 210 minutes.


Then the distance between the cities, according to the equation (1), is 

    100*210 + 80*210 = 37800 meters = 37.8 kilometers.


<U>Answer</U>.  The distance between the cities is 37800 meters, or 37.8 kilometers.
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