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?
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To find the distance between Seattle and the wilderness, we can use the formula:
Distance = Speed × Time
Let's denote the distance from Seattle to the wilderness as "d" (in miles).
On the outbound trip, the average speed of the private plane was 220 mph. The time it took to travel this distance can be calculated as:
Time = Distance / Speed
Time = d / 220
On the return trip, the average speed was 264 mph. The time for the return trip can be calculated as:
Time = Distance / Speed
Time = d / 264
Given that the total traveling time was 5 hours, we can write the equation:
Time (outbound) + Time (return) = 5
Therefore:
d / 220 + d / 264 = 5
To solve this equation, we can find a common denominator and then combine the fractions:
(264d + 220d) / (220 × 264) = 5
484d / 58080 = 5
Now, we can solve for d:
484d = 5 * 58080
484d = 290400
d = 290400 / 484
d ≈ 600 miles
Therefore, the distance between Seattle and the wilderness is approximately 600 miles.