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Archy [21]
3 years ago
7

Two cars, car X and car Y , start moving from the same point P on a cross intersection. Car X is travelling east and car Y is tr

avelling north. Some time later car X is 60 km east of point P and travelling in an easterly direction at 80 km/h and car Y is 80 km north of point P and travelling in a northerly direction at 100 km/h. How fast is the distance between car X and car Y changing?
Mathematics
1 answer:
agasfer [191]3 years ago
5 0
Let the distance traveled by car X be x km 
<span>let the distance traveled by car Y by y km </span>
<span>their paths form a right-angled triangle. </span>
<span>Let the distance between them be D km </span>
<span>D^2 = x^2 + y^2 </span>
<span>2D dD/dt = 2x dx/dt + 2y dy/dt </span>
<span>dD/dt = (x dx/dt + y dy/dt)/D </span>

<span>at the given case: </span>
<span>x = 60, y = 80 , dx/dt = 80, dy/dt = 100 </span>
<span>D^2 = 60^2 + 80^2 = 10000 </span>
<span>D = 100 </span>

<span>dD/dt = (60(80) + 80(100))/100 </span>
<span>= 128 </span>
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