A private plane traveled from Seattle to a rugged wilderness, at an average speed of 420 mph. On the return trip, the average speed was 300mph. If the total traveling time was 6 hours, how far is Seattle from the wilderness?
let the distance from Seattle to wilderness be x miles
x/420 + x/300 = 6
times 2100 the LCM
5x + 7x = 12600
x = 1050 miles
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 represented by D miles.
On the outbound trip, the plane traveled at an average speed of 420 mph, so the time taken for this trip can be calculated using the formula:
Time = Distance / Speed
Therefore, the time for the outbound trip can be expressed as:
Time(outbound) = D / 420
On the return trip, the average speed was 300 mph, so the time taken for this trip can be calculated using the formula:
Time = Distance / Speed
Therefore, the time for the return trip can be expressed as:
Time(return) = D / 300
The total traveling time is given as 6 hours, so we can write the equation:
Time(outbound) + Time(return) = 6
Substituting the expressions for the time calculations, we get:
D/420 + D/300 = 6
To solve this equation, we can find a common denominator and then simplify:
(300D + 420D) / (300 * 420) = 6
720D / 126000 = 6
Cross-multiplying and solving for D:
720D = 6 * 126000
D = (6 * 126000) / 720
D ≈ 1050 miles
Therefore, Seattle is approximately 1050 miles from the wilderness.