Question

SCALCET8 3.9.017.MI. Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing two hours later

Answer 1

The rate at which the distance between the cars increasing two hours later=52mi/h

Explanation:

Let

Speed of one car, x'=48 mi/h

Speed of other car, y'=20 mi/h

We have to find the rate at which the distance between the cars increasing two hours later.

After 2 hours,

Distance traveled by one car

`x=48* 2=96 mi`

Using the formula

`Distance=Time* speed`

Distance traveled by other car

`y=20* 2=40 mi`

Let z be the distance between two cars after 2 hours later

`z=√(x^2+y^2)`

Substitute the values

`z=√((96)^2+(40)^2)`

z=104 mi

Now,

`z^2=x^2+y^2`

Differentiate w.r.t t

`2z(dz)/(dt)=2x(dx)/(dt)+2y(dy)/(dt)`

`z(dz)/(dt)=x(dx)/(dt)+y(dy)/(dt)`

Substitute the values

`104(dz)/(dt)=96* 48+40* 20`

`(dz)/(dt)=(96* 48+40* 20)/(104)`

`(dz)/(dt)=52mi/h`

Hence, the rate at which the distance between the cars increasing two hours later=52mi/h