QuestionFind the function $d(t)$ for a car that travels 372 miles in 6 hours from Lubbock to Austin.

Studdy Solution

STEP 1

Assumptions1. The total distance traveled is372 miles. . The total time taken is6 hours.
3. The car travels at a constant speed.

STEP 2

We need to find the speed of the car first, which is the ratio of the total distance traveled to the total time taken. The formula for speed is $Speed = \frac{Total\, distance}{Total\, time}$

STEP 3

Now, plug in the given values for the total distance and total time to calculate the speed.
$Speed = \frac{372\, miles}{6\, hours}$

STEP 4

Calculate the speed of the car.
$Speed = \frac{372\, miles}{6\, hours} =62\, miles/hour$

STEP 5

The function $d(t)$ that describes the distance $d$ in miles that the car has traveled after $t$ hours since its departure from Lubbock is given by the product of the speed and time. The formula for $d(t)$ is $d(t) = Speed \times Time$

STEP 6

Now, plug in the value for the speed into the formula for $d(t)$ .
$d(t) =62\, miles/hour \times t$ So, the function $d(t)$ that describes the distance $d$ in miles that the car has traveled after $t$ hours since its departure from Lubbock is $d(t) =62t$

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