Question

Richard is driving home to visit his parents. 135 mi of the trip are on the interstate highway where the speed limit is 65 mph . Normally Richard drives at the speed limit, but today he is running late and decides to take his chances by driving at 73 mph .

Answer 1

Answer:

He saves 13.2 minutes

Explanation:

Hey! The question is incomplete, but it can be found on the internet. The question is:

How many minutes did he save?

Let's call:

$t_{1}:Time \ at \ speed \ 65mph \\ \\ t_{2}:Time \ at \ speed \ 73mph \\ \\ v_{1}=65mph \\ \\ v_{2}=73mph$

We know that the 135 miles are on the interstate highway where the speed limit is 65 mph. From this, we can calculate the time it takes to drive on this highway. Assuming Richard maintains constant the speed:

$v=\frac{d}{t} \\ \\ d:distance \\ \\ t:time \\ \\ v:velocity \\ \\ t_{1}=\frac{d}{v_{1}} \\ \\ t=\frac{135}{65} \\ \\ t_{1}=2.07 \ hours$

Today he is running late and decides to take his chances by driving at 73 mph, so the new time it takes to take the trip is:

$t_{2}=\frac{135}{73} \\ \\ t_{2}=1.85 \ hours$

So he saves the time $t_{s}$:

$t_{s}=t_{1}-t_{2}=2.07-1.85=0.22 \ hours$

In minutes:

$t_{s}=0.22h\left(\frac{60min}{1h}\right) \\ \\ \boxed{t_{s}=13.2min}$