Question

A train travels due north at 40 mph. A car travels toward the train from the same starting point leaving 2 hours later than the train.

If the car is traveling at 60 mph, how many miles will the car have to travel to catch up to the train?

Answer 1

train: (h+2)*40
car: h*60

when does the car catch up to the train?
train=car
(h+2)*40=h*60
40h+80=60h
80=20h
4=h

How many miles did the car drive after h=4 hours/when it catches the train?
4*60=240 miles

Answer 2

The distance traveled by car has to travel to catch up to the train is 240 miles.

Given that,

A train travels due north at 40 mph.

A car travels toward the train from the same starting point leaving 2 hours later than the train.

If the car is traveling at 60 mph.

We have to determine,

How many miles will the car have to travel to catch up to the train?

According to the question,

The distance will the car have to travel to catch up to the train is determined by using the following formula;

$\rm Speed = \dfrac{Distance}{Time}$

Let the distance will the car have to travel to catch up to the train be x.

Then,

The distance traveled by car in times t is,

$\rm Speed = \dfrac{Distance}{Time}\\\\Distance = Speed \times Time\\\\ x = 40 \times t\\\\x = 60t$

And car travels toward the train from the same starting point leaving 2 hours later than the train.

Then,

The distance traveled by train in time (t+2) is,

$\rm Speed = \dfrac{Distance}{Time}\\\\Distance = Speed \times Time\\\\ x = 40 \times( t+2)\\\\x = 40(t+2)$

Substitute the value of x in equation 2 from equation 1,

$\rm x = 40(t+2)\\\\60t=40t+80\\\\60t-40t=80\\\\20t=80\\\\t = \dfrac{80}{20}\\\\t = 4$

Therefore,

The distance traveled by car has to travel to catch up to the train is,

$\rm x = 60t\\\\x = 60\times 4\\\\x = 240 \ miles$

Hence, The distance traveled by car has to travel to catch up to the train is 240 miles.

To know more about System of Equation click the link given below.

https://brainly.com/question/12895249