Question

A truck enters a highway driving 60 mph. A car enters the highway at the same place 11 minutes later and drives 71 mph in the same direction. From the time the car enters the​ highway, how long will it take the car to pass the​ truck?

Answer 1

The car passed the truck after 60 minutes.

Explanation:

We should first find how far the truck was from the entrance to the highway when the car entered (after 11 minutes). We know that the distance travelled is the product of the time and speed, therefore, the location of the truck is given by
`d = 60 * 11 = 660`.

Now we can build functions representing the distance from the entrance of both vehicles, in respect to the time travelled.

Truck's Function

`x_0 = 660m \\ v = 60mph \\ \to x(t) = 660m + 60t`

Car's Function

`x_0 = 0m \\ v = 71mph \\ \to x(t) = 71t`

Finally, we can equalize both functions to find out at what time the car passed the truck (when their graphs intercepted):

`660 + 60t = 71t \\ \to 660 = 11t \\ \to t = 60m`