Question

Traveling with a speed of 70 mph, a car covered a distance D miles in T hours. Write an equation that relates the distance D this car travels in T hours. Use the equation to find the distance the car travels between 3:30 p.m. and 5:00 p.m. Please write the formula with variables.

Answer 1

Formula: Distance= Speed * Time

Distance= 70 * T

T=1.5 hrs

D= 70*1.5

D=130 miles

Answer 2

Part A)
`D=70T`

Part B)
`D=105\ miles`

Explanation:

Par A) Write an equation that relates the distance D this car travels in T hours

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

The speed is a proportional relationship between the distance and the time

Let

D ----> the distance in miles

T ----> the time in hours

so

`D=kT`

In this problem the constant of proportionality k represent the speed of the car in miles per hour

we have

`k=70\ mi/h`

substitute

`D=70T`

Part B) Use the equation to find the distance the car travels between 3:30 p.m. and 5:00 p.m

we know that

The time between 3:30 p.m. and 5:00 p.m is equal to

5:00 p.m-3:30 p.m=1.5 hours

so

For T=1.5 h

substitute in the equation and solve for D

`D=70(1.5)`

`D=105\ miles`