Question

Two equations are written to express how far a car can go when driving on different roads on Road 1 the car can go 60 miles in 2 hours on road to the car can go 90 miles in 4 hours write an equation where Y is the distance in miles and X is the time in hours to represent the motion of the faster car

Answer 1

To express the motion of the faster car in an equation, we first need to determine its speed.

For the car on Road 1:
- It travels 60 miles in 2 hours.
- The speed (s) can be calculated as:
\[
s = \frac{\text{distance}}{\text{time}} = \frac{60 \text{ miles}}{2 \text{ hours}} = 30 \text{ miles per hour}
\]

For the car on Road 2:
- It travels 90 miles in 4 hours.
- The speed for this car is:
\[
s = \frac{90 \text{ miles}}{4 \text{ hours}} = 22.5 \text{ miles per hour}
\]

Since the faster car is on Road 1, its speed is 30 miles per hour.

Now we can write the equation to represent the motion of the faster car, where \(Y\) is the distance in miles and \(X\) is the time in hours.

The general equation for distance is:
\[
Y = \text{speed} \times \text{time}
\]

Substituting the speed of the faster car:
\[
Y = 30X
\]

This equation means that for every hour (X) the car drives, it travels 30 miles (Y).