Question

a car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in t hours.
a. complete the statement about the meaning of 65 in this situation.
the car travels miles in hour.
b. how many miles does the car travel in 1.5 hours? miles
c. how long does it take the car to travel 26 miles at this speed? minutes

Explanation:

Step1: Analyze the speed - distance formula

The formula $d = 65t$ is in the form of $d=vt$ (where $v$ is speed and $t$ is time), so the speed $v = 65$ miles per hour. That means the car travels 65 miles in 1 hour.

Step2: Find distance for $t = 15$ hours

Substitute $t = 15$ into $d=65t$. Then $d=65\times15=975$ miles.

Step3: Find time for $d = 20$ miles

First, from $d = 65t$, we can solve for $t$ when $d = 20$. So $t=\frac{d}{65}=\frac{20}{65}=\frac{4}{13}$ hours. Since 1 hour = 60 minutes, then $t=\frac{4}{13}\times60=\frac{240}{13}\approx18.46$ minutes.

Answer:

a. 65, 1
b. 975
c. $\frac{240}{13}$