Question

Two cars are heading toward the same intersection. Car A travels due east at 20 miles per hour, and Car B travels due north at 50 miles per hour. At what rate, in miles per hour, is the distance between the two cars decreasing when Car A is 0.375 miles from the intersection and Car B is 0.5 miles from the intersection?
a. 35 mph
b. 46 mph
c. 52 mph
d. 70 mph

Answer 1

Answer:

Option C - 52 mph

Step-by-step explanation:

I've attached an image to depict the diagram of movement of both cars.

dy/dt = 50 mph

dx/dt = 20 mph

From the attached image, using pythagoras theorem, we have;

x² + y² = s²

Differentiating with respect to to using implicit differentiation with power rule, we have;

2x(dx/dt) + 2y(dy/dt) = 2s(ds/dt)  - - (eq1)

Now, let's find s by pythagoras theorem.

s² = 0.375² + 0.5²

s² = 0.390625

s = √0.390625

s = 0.625

Plugging in all the relevant values into eq 1,we have;

2×0.375(20) + 2×0.5(50) = 2×0.625(ds/dt)

15 + 50 = 1.25(ds/dt)

65 = 1.25(ds/dt)

ds/dt = 65/1.25

ds/dt = 52 mph