A private plane traveled from Seattle to a rugged​ wilderness, at an average speed of 220 mph. On the return​ trip, the average speed was 264mph. If the total traveling time was 5 hours, how far is Seattle from the​ wilderness?

http://www.jiskha.com/display.cgi?id=1480220641

To find the distance between Seattle and the wilderness, we can use the formula: Distance = Speed * Time.

Let's assume the distance from Seattle to the wilderness is D miles.

On the outbound trip, the plane traveled at an average speed of 220 mph, and the time taken is D/220 hours.

On the return trip, the plane traveled at an average speed of 264 mph, and the time taken is D/264 hours.

The total travel time is given as 5 hours.

So we can write the equation: D/220 + D/264 = 5.

To solve this equation, we can multiply it through by the least common multiple (LCM) of the denominators, which is 2,640.

(2,640 * D)/220 + (2,640 * D)/264 = 2,640 * 5.

Since 2,640 is divisible by both 220 and 264, this equation simplifies to:

12D + 10D = 13,200.

22D = 13,200.

Dividing both sides by 22, we get:

D = 13,200/22.

D = 600.

Therefore, the distance between Seattle and the wilderness is 600 miles.