SOLUTION: A plane was scheduled to fly from Atlanta to Washington, D.C. The plan flies at a constant speed of 150 miles per hour. However, the flight was against a head wind of 10 mph. The t

Question 1071608: A plane was scheduled to fly from Atlanta to Washington, D.C. The plan flies at a constant speed of 150 miles per hour. However, the flight was against a head wind of 10 mph. The threat of mechanical failure forced the plan to turn back, and it returned to Atlanta with a tail wind of 10 miles per hour, landing 1.5 hours after it had taken off. How far had the plane traveled before turning back?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A plane was scheduled to fly from Atlanta to Washington, D.C. The plan flies at a constant speed of 150 miles per hour.
However, the flight was against a head wind of 10 mph.
The threat of mechanical failure forced the plan to turn back, and it returned to Atlanta with a tail wind of 10 miles per hour, landing 1.5 hours after it had taken off.
How far had the plane traveled before turning back?
:
150 - 10 = 140 mph, effective speed against the wind
150 + 10 = 160 mph, effective speed with the wind
:
let d = the one-way distance to the point of return
:
Write a time equation, time = dist/speed
time out + time back = 1.5 hrs
+ = 1.5
multiply equation by LCM of 140 and 160, 1120
1120* + 1120* = 1120(1.5)
cancel the denominators
8d + 7d = 1680
d = 1680/15
d = 112 mi from Atlanta when it turned back
:
;
Confirm this, find the actual time each way
112/140 = .8 hrs
112/160 = .7 hrs
----------------
tot time: 1.5 hrs

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