Question

a car travels at a constant speed of 45 miles per hour. the distance the car travels in miles is a function of time t, in hours, given by d(t)=45t. find the inverse function by expressing the time of travel in terms of the distance traveled. call this function t(d).
t(d)=

find t(170). round to 1 decimal place.
t(170)=

interpret the meaning.
when the car travels for 170 hours, it has traveled t(170) miles.
when the car travels 170 miles, it has traveled for t(170) hours.
question help: video

Explanation:

Step1: Find inverse function

Given $d(t)=45t$, solve for $t$ in terms of $d$. Divide both sides by 45: $t=\frac{d}{45}$, so $t(d)=\frac{d}{45}$.

Step2: Evaluate $t(170)$

Substitute $d = 170$ into $t(d)$: $t(170)=\frac{170}{45}\approx3.8$.

Answer:

$t(d)=\frac{d}{45}$
$t(170)=3.8$
When the car travels 170 miles, it has traveled for $t(170)$ hours.