Question 1180675
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Since the two trains are traveling in directions that differ by 90 degrees, the line joining the positions of the two trains at any time forms a right triangle with the paths of the trains.  So solve using the Pythagorean Theorem.<br>
x = slower train speed (km/h)
x+5 = faster train speed (km/h)
2x = distance (km) slower train travels in 2 hours
2x+10 = distance (km) faster train travels in 2 hours<br>
After 2 hours, the right triangle has legs of 2x and 2x+10 and a hypotenuse of 50:<br>
{{{(2x)^2+(2x+10)^2 = 50^2}}}
{{{4x^2+(4x^2+40x+100) = 2500}}}
{{{8x^2+40x-2400 = 0}}}
{{{x^2+5x-300 = 0}}}
{{{(x+20)(x-15) = 0}}}<br>
{{{x = -20}}} or {{{x = 15}}}<br>
Obviously reject the negative solution, since the speeds of the trains are not negative.<br>
ANSWER: The average speeds of the two trains are x=15km/h and x+5=20km/h<br>