On a vacation, Sarah averaged 40 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, she averaged 60 mph. What is the distance between the two cities if her total traveling time was 30 hours?

The distance between the two cities is 720 miles

Step-by-step explanation:

Here, we want to calculate the distance between the two cities

Since the speed on both legs of the journey is not the same, it means she will take less time traveling the same distance at a higher speed

Mathematically, distance = speed * time

Let the time spent going be x hours

The time spent coming will be (30-x) hours since 30 is the total

The distance of going will be;

40 * x = 40x

The distance of coming will be;

60(30-x)

Since these distances are equal, we equate both;

40x = 60(30-x)

40x = 1800 - 60x

60x + 40x = 1800

100x = 1800

x = 1800/100

x = 18 hours

The distance = 40 mph * 18 h = 720 miles

step-by-stp

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