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A railroad track and a road cross at right angles. An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60 meters per second. At how many meters per second is the train moving away from the observer 4 seconds after it passes through the intersection?

Verified Answer :

Simple related rates problem. 

First use the Pythagorean theorem. a^2 + b^2 = c^2 

then take the first derivative of it to get 

2a(a') + 2b(b') = 2c(c') 

Now figure out how far the train is after 4 seconds 

60(4)=240 
70^2 + 240^2 = c^2 
c = 250 

Now plug in the variables you know 

2(70)0 + 2(240)60 = 2(250)c' and solve for c' or the rate of change of c. 

57.6 or A 

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