A private plane traveled from Seattle to a rugged wilderness at an average speed of 180 mph. The return trip speed s 225 mph. If the total travelling time was 7 hours, how far is Seattle from the wilderness
Not quite, Fiona. When you finally got an answer, you ought to have done just a sanity check. The average speed was somewhere near 200 mph, and the flew for 7 hours, a distance of 57 mile is ludicrous.
since time = distance/speed, and the total time was 7 hours, then we want to find the distance d such that
d/180 + d/225 = 7
d = 700 miles
Let's assume the distance between Seattle and the wilderness is 'd' miles.
We know that time equals distance divided by speed.
For the trip from Seattle to the wilderness:
The average speed is 180 mph, and the time taken is d/180 hours.
For the return trip:
The speed is 225 mph, and the time taken is d/225 hours.
We are given that the total traveling time is 7 hours. So, we can set up the equation as follows:
d/180 + d/225 = 7
To solve the equation, we can find a common denominator for the fractions. In this case, the least common multiple (LCM) of 180 and 225 is 900.
Multiplying the equation by 900, we get:
900 * (d/180) + 900 * (d/225) = 900 * 7
Simplifying further:
5d + 4d = 6300
9d = 6300
d = 700
Therefore, Seattle is 700 miles away from the wilderness.
To find the distance between Seattle and the wilderness, we can use the formula:
Distance = Speed * Time
Let's denote the distance between the two locations as "d".
We know that the average speed from Seattle to the wilderness is 180 mph. Let's calculate the time it took to travel from Seattle to the wilderness:
Time1 = Distance / Speed1
Time1 = d / 180
Next, we know that the return trip speed from the wilderness to Seattle is 225 mph. Let's calculate the time it took to travel from the wilderness to Seattle:
Time2 = Distance / Speed2
Time2 = d / 225
According to the problem, the total traveling time is 7 hours. Therefore, the sum of Time1 and Time2 is 7:
Time1 + Time2 = 7
(d / 180) + (d / 225) = 7
Now we can solve this equation to find the value of "d," which represents the distance between Seattle and the wilderness.
Seattle to wilderness=180mph
wilderness to Seattle=225mph
225+180=405miles in 7 hrs
405/7=57.8571 mph
57.8571 miles