Question

When Mr. Crain was driving to work in the morning, there was heavy traffic, so he was traveling at a speed of 25 mph. When he was coming back after work there where no traffic, so he drove at a speed of 45 mph. Find the distance from Mr. Crain's home to his office, if it took him 20 more minutes to get to work than to drive home.

Answer 1

let the distance from home to work be x;
time=distance/speed
Time taken to travel to work is:
time=x/25
Time taken to reach home from work:
time=x/45
given that it took him 20 min more to travel to work than going home we shall have:
x/25-x/45=20/60
solving for x we get:
x=75/4=18.75 miles

Answer 2

The distance from the office to the home is 18.75 miles.

Given, the speed of a vehicle travelling to the office from home is 25 mph and the speed of a vehicle travelling to the home from the office is 45 mph.

Let us assume that the distance from the office and the home of Mr. Crain are x miles and the time taken by Mr. Crain to reach the home from the office is t hours.

Now, it took him 20 more minutes to get to work than to drive home.

Thus, time is taken by him to reach from home to office is (t hours and 20 minutes)

Therefore,

$t\;\rm{hours}\;and \;20 \;minutes=t\frac{1}{3}\\=\frac{3t+1}{3}$

Now the formula for finding the speed of a body is mentioned below:

$\rm{Speed}=\dfrac{Distance}{Time}$

Now, apply the formula while travelling office from the home.

${45}=\dfrac{x}{t}\\t=\dfrac{x}{45}$

Now, apply the formula while travelling home from the office.

$\rm{25}=\dfrac{x}{(3t+1)/3}$

Now, substitute the value of t and solve the above expression further.

$\begin{aligned}\rm{25}&=\dfrac{x}{(3x/45+1)/3}\\25&=\dfrac{3x}{x/15+1}\\25&=\dfrac{45x}{x+15}\\25x+375&=45x\\20x&=375\\x&=18.75\;\rm{miles} \end{aligned}$

Thus, the distance from the office to the home is 18.75 miles.

To know more about the speed, please refer to the link:

https://brainly.com/question/14615467