Description
A man flies a small airplane from Fargo to Bismarck, North Dakota—a distance of 180 mi. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 h 15 min. What is his speed in still air, and how fast is the wind blowing?
speed in still air | mph |
wind speed | mph |
Explanation & Answer
Let speed of plane x miles/hr and speed of still air = y miles/hr
speed = distance/time ;
while travelling along the wind time required = 1 hr 15 minutes or 1.25 hrs
while traveling along the wind (x+y) = 180/1.25 or x+y = 144 -------------(1)
while travelling against wind x-y = 180/2 or x-y = 90 -------------(2)
Adding Eq 1 & 2 we get2x =234 hence x = 117 miles/hr
therefore y = 27 miles/hr
Answer
speed in still air : 117 mph