Question

A truck enters a highway driving 60 mph. A car enters the highway at the same place 5 minutes later and drives 73mph 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

Car takes 23.076 minute to pass the truck

Solution:

A truck enters a highway driving 60 mph

A car enters the highway at the same place 5 minutes later and drives 73mph in the same direction

Let us consider,

Truck speed = 60 mph ( given )

Time for the truck = T hour

The distance is given as:

`distance = speed * time`

Therefore,

`distance = 60 * T\\\\Distance = 60T ------- eqn 1`

Let us consider

Car speed = 73 mph ( given )

car time = T - 5minutes

We know that,

1 hour = 60 minutes

Therefore,

`Car\ time = T - (5)/(60)\ hour\\\\Car\ time = T - (1)/(12)\ hour`

Distance of car:

`Distance = 73 * (T - (1)/(12)) ------ eqn 2`

The two distances are equal:

`60T = 73(T - (1)/(12))\\\\60T = 73T - (73)/(12)\\\\60T = 73T - 6.0833\\\\73T - 60T = 6.0833\\\\13T = 6.0833\\\\Divide\ both\ sides\ by\ 13\\\\T = 0.4679`

How long will it take the car to pass the​ truck?

`Car\ time = T - (1)/(12)\ hour\\\\Car\ time = 0.4679 - 0.0833\\\\Car\ time = 0.3846\ hour\\\\Car\ time = 23.076\ minute`

Thus car takes 23.076 minute to pass the truck