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Runner A is initially 5.6 km west of a flagpole and is running with a constant velocity of 8.4 km/h due east.
Runner B is initially 4.9 km east of the flagpole and is running with a constant velocity of 7.5 km/h due west.
How far are the runners from the flagpole when their paths cross?
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Lat assume that the flag pole is the zero point on x-axis directed from west to east.
Then the coordinate of the 1st runner in time is -5.6 + 8.4*t kilometers;
the coordinate of the 2nd runner in time is 4.9 - 7.5*t kilometers,
where t is the time from the start, in hours.
The runners are in the crossing point when
-5.6 + 8.4t = 4.9 - 7.5t.
Simplify this equation and find t
8.4t + 7.5t = 4.9 + 5.6
15.9t = 10.5
t = 10.5/15.9 = 0.660377358 of an hour.
The coordinate of the crossing point is x = -5.6 + 8.4*0.660377358 = -0.052830193 kilometers,
or 52.83 meters west from the flag pole. The numbers are approximate.
Solved.
