Question

The only available flight from Logan Airport to Denver, Colorado must stop in Chicago. The distance between Boston and Chicago is 55 miles less than the distance between Chicago and Denver. The total distance flown from Boston to Chicago to Denver is 1767 miles. Find the distance between Boston and Chicago, and between Chicago and Denver.

Please show your work!

Answer 1

the distance between Boston and Chicago is 856 miles, and the distance between Chicago and Denver is (856 + 55) = 911 miles.

Explanation:

According to the given information, the distance between Chicago and Denver is 55 miles more than the distance between Boston and Chicago. So, the distance between Chicago and Denver is (x + 55) miles.

The total distance flown from Boston to Chicago to Denver is 1767 miles. So, we can write the equation:

Distance from Boston to Chicago + Distance from Chicago to Denver = Total distance

x + (x + 55) = 1767

Now, let's solve the equation:

2x + 55 = 1767

2x = 1767 - 55

2x = 1712

x = 1712/2

x = 856

Answer 2

The distance between Boston and Chicago is 856 miles, and the distance between Chicago and Denver is 911 miles.

Explanation:

Let's assume the distance between Boston and Chicago is x miles.

According to the given information, the distance between Chicago and Denver is 55 miles more than the distance between Boston and Chicago. So, the distance between Chicago and Denver is (x + 55) miles.

The total distance flown from Boston to Chicago to Denver is 1767 miles. This can be expressed as the sum of the distances between each pair of cities:

Boston to Chicago + Chicago to Denver = 1767

x + (x + 55) = 1767

Simplifying the equation:

2x + 55 = 1767

Subtracting 55 from both sides:

2x = 1712

Dividing both sides by 2:

x = 856

Therefore, the distance between Boston and Chicago is 856 miles, and the distance between Chicago and Denver is (856 + 55) = 911 miles.