Answer:
d(L)/dt = 9,43 miles per hour
Step-by-step explanation:
As Charles and Maria travel in perpendicular directions, these directions could be considered as two legs ( x and y ) of a right triangle and distance (L) between them as the hypotenuse, therefore, according to Pythagoras theorem
L² = x² + y²
And as all ( L , x , and y ) are function of time, we apply differentiation in both sides of the equation to get
2* L d(L)/dt = 2*x*d(x)/dt + 2*y*d(y)/dt (1)
In equation (1) we know:
d(x)/dt = 8 miles/per hour ( Maria )
d(y)/dt = 5 miles /per hour (Charles)
In 3 hours time Maria has travel 3*8 = 24 miles
And Charles 5*3 = 15 miles
Then at that time L is equal to
L = √ 24² + 15² ⇒ L = √ 576 + 225 ⇒ L = √801 ⇒ L =28,30 miles
Then plugging these values in equation (1)
2* L d(L)/dt = 2*x*d(x)/dt + 2*y*d(y)/dt
2* 28.30 * d(L)/dt = 2*24*8 + 2* 15*5
56.6 *d(L)/dt = 384 + 150
d(L)/dt = 534/56,6
d(L)/dt = 9,43 miles per hour
