Problema Solution
A jet flew at an average of 480mph from point x to point y . Because of head winds the jet averaged only 460 mph on the return trip and the return trip took 10 mins longer. How many hours from point Y to point X ? How far is it from point X to point Y
Answer provided by our tutors
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p = the plane's speed in still air
w = the speed of the wind
d = the distance from point X to point Y
t1 = the time from X to Y
t2 = the time from Y to X (return trip with head wind)
the speed of the plane traveling with head wind is: p - w = 460 mph
the speed of the plane traveling with the wind is: p + w = 480 mph
the return trip and the return trip took 10 mins longer
t2 = t1 + 10/60
t2 = t1 + 1/6
since speed (or rate) = distance/time => distance = speed*time
when traveling with head wind:
d = (p - w)t2
(p - w)t2 = d
460*t2 = d => t2 = d/460
when traveling with the wind t2 = t1 + 1/6
d = (p + w)t1
480*t1 = d => t1 = d/480
plug t1 = d/480 and t2 = d/460 into t2 = t1 + 1/6
d/460 = d/480 + 1/6
by solving the equations we find
d = 1850 miles is the distance between X and Y
click here to see the step by step solution of the equation
t2 = 460/1850 = 46/185 = 0.2486 h
t2 = 14.9 min
the plane traveled 0.2486 hours from point Y to point X.