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
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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?
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
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tot time: 1.5 hrs
