A private plane traveled from Seattle to the rugged wilderness at a average speed of 176 mph. on the return trip the average speed was 308 mph. if the total traveling time was 5 hours. How far is Seattle to the wilderness?
please help
let the distance be x miles
time for first leg = x/176
time for return leg = x/308
solve for x:
x/176 + x/308 = 5
multiply by 1232 , the LCM
7x + 4x = 6160
x = 560 miles
To find the distance between Seattle and the rugged wilderness, we can use the formula:
Distance = Speed x Time
Let’s assume the distance from Seattle to the wilderness is 'd' miles.
On the outbound trip, the average speed of the plane is 176 mph. Let's assume the time taken for this trip is 't' hours.
So, the distance covered on the outbound trip is: Distance = Speed x Time --> d = 176t.
On the return trip, the average speed of the plane is 308 mph. The time taken for this trip would be 5 - t hours, as the total traveling time is 5 hours.
Therefore, the distance covered on the return trip is: Distance = Speed x Time --> d = 308(5 - t).
Since the distance from Seattle to the wilderness is the same for both the outbound and return trips, we can equate the two distances:
176t = 308(5 - t).
Now, let's solve this equation to find the value of 't' and then substitute it back to find the distance 'd'.
176t = 308(5 - t)
176t = 1540 - 308t
484t = 1540
t = 1540/484
t ≈ 3.18 hours
Now that we have the value of 't', we can substitute it into either equation to find the distance 'd'. Let's use the first equation:
d = 176t
d ≈ 176(3.18)
d ≈ 558.88 miles
Therefore, the distance from Seattle to the rugged wilderness is approximately 558.88 miles.