Question

At noon a truck leaves Prescott, AZ driving east at a speed of 40 miles per hour. An hour later, a second truck leaves Prescott driving north at a speed of 60 miles per hour. At what rate is the distance between the trucks increasing at 2:00 P.M. that day?

Answer 1

Answer: 60 miles per hour

Explanation:

The right angle triangle formed is shown in the attached photo.

Let the first truck be truck A and the second truck be truck B

At noon, truck A moved from Prescott, AZ at a speed of 40 miles per hour. It travelled for one hour before truck A moved.

Distance = speed × time.

This means that distance moved by truck A in one hour is 40 × 1 = 40 miles. So at 1 pm, truck A had moved 40 miles. At 2pm, truck A would have moved another 40 miles because it's another one hour and the speed is still 40 miles per hour. Total distance moved by truck A at 2pm = 40 + 40 = 80 miles

At 1 pm, truck B moved for one hour at a speed of 60 miles per hour.

Distance moved by truck B = 60 × 1 = 60 miles.

So at 2pm, truck be has moved 60 miles.

To determine the distance,x between them at 2pm, we will find the hypotenuse of the triangle.

x^2 = √(80^2 + 60^2)

x = 100 miles

So at 2pm, they are already 100 miles apart.

So at 1pm, they were 40 miles apart and 1 hour later, at 2pm, they were 100 miles apart. Therefore, the distance increased by 60 miles per hour at 2pm