Question

Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 36 mi/h. At what rate is the distance between the cars increasing three hours later?

Answer 1

Answer:

rate is the distance between the cars increasing three hours later 60mi/h

Explanation:

given data

travels south = 48 mi/h

travels west = 36 mi/h

solution

As the right angle triangle.

we consider here length the shorter leg(west) = x

and length the longer leg(south) = y

and the hypotenuse = z

so we apply here Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²     ...................1

that is express as

z² = x² + y²   .................2

so we get here rate by which here distances is changing

so that we do differentiate with respect to t that is

2z $\frac{dz}{dt}$ = 2x $\frac{dx}{dt}$ + 2y $\frac{dy}{dt}$       .................3

so as we know Distance = speed × time   ...................4

x = 36 × 3 = 108 miles

y = 48 × 3 = 144 miles

so put value in equation 2

z² = 108² + 144²

z²  = 32400

z = 180 miles

put these value in equation 3 we get

2 × 180 × $\frac{dz}{dt}$ = 2 × 108 × 36 + 2 × 144 × 48

solve we get

$\frac{dz}{dt}$ = 60 mi/h