The car traveled all the way between the two cities in three days. On the first day, the car traveled 7/20 of the total distance

The car traveled all the way between the two cities in three days. On the first day, the car traveled 7/20 of the total distance, on the second day – 8/13 of the remaining distance, and on the third day the car traveled 72 km less than in the first day. What is the distance between cities?

Let w be the distance between cities.
On the first day, the car drove 7/20 all the way. Let’s find out how many kilometers she traveled.
7/20 * w = 7w / 20 (km).
So, on the first day, the car drove 7w / 20 km. Let’s find out how many kilometers she has left to travel after the first day of travel.
w – 7w / 20 = 20w / 20 – 7w / 20 = 13w / 20 (km).
So, after the first day of the journey, the car has to drive 13w / 20 km. And on the second day, she drove 8/13 of the remaining way. Let’s find out how many kilometers the car drove on the second day.
13w / 20 * 8/13 = 8w / 20 = 2w / 5 (km).
We already know that on the first day the car drove 7w / 20 km. And on the third day she drove 72 km less. Therefore, on the third day, the car drove 7w / 20 – 72 km.
Thus, the car has passed:
7w / 20 kilometers on the first day;
2w / 5 kilometers on the second day;
7w / 20 – 72 kilometers on the third day;
w kilometers in all three days.
We can make an equation.
7w / 20 + 2w / 5 + (7w / 20 – 72) = w.
Let us bring the fractions to a common denominator.
7w / 20 + 8w / 20 + 7w / 20 – 72 = w;
22w / 20 – 72 = w.
Reduce 22w / 20 by two.
11w / 10 – 72 = w.
Move the number 72 to the right side of the equation and w to the left side.
11w / 10 – w = 72;
11w / 10 – 10w / 10 = 72;
w / 10 = 72.
Multiply both sides of the equation by ten to get rid of the denominator.
w = 72 * 10;
w = 720.
We found out that the cities are located at a distance of 720 km from each other.
Answer: 720 kilometers.