rate and distance

Question

A truck enters the highway driving 60mph. a car enters the highway at the same place 14 minutes later driving 70mph in the same direction.  from the time the car enters the highway, how long will it take the car to pass the truck? round to the nearest minute.

Answer 1

Brooke,

 

Let's look at the truck first.

 

The truck's rate is 60 mph.  Since it's driving on this hwy for 14 minutes before the car enters, let's look at the distance travelled in two pieces: 

1) the first 14 minutes

2) the rest of the trip until the car passes the truck.

 

truck distance = 60(14/60) + 60t

 

Now the car enters at a rate of 70 mph

Car distance = 70t

 

We want to know how long it takes the car to pass the truck.  So at what time after the car enters the highway, will the distance of the car equal the distance of the truck?

 

60(14/60) + 60t = 70t

14 = 10t

1.4 = t

So the car will pass the truck after 1.4 hours

 

1.4 hours • 60 min/hour = 84 minutes or 1 hour 24 minutes.