Question

The flight distance from Cincinnati, Ohio, to Chicago, Illinois, is approximately 300 mi. On a recent round-trip between these cities in my private plane, I encountered a steady 25 mph headwind on the way to Chicago, with a 25 mph tailwind on the return trip. If my total flying time came to exactly 5 hr, what was my flying time to Chicago? What was my flying time back to Cincinnati? (Hint: The flight time between the two cities must add up to 5 hr.)

Answer 1

well you need to know the speed of the plane.
distance = rate*time
Let x be speed of plane, t1the time it took to Chicago, t2 the time to return to Cinci
t1 + t2 = 5 --> t1 = 5-t2
trip to Chicago:
300/t1 = x-25 --> x = 300/t1 +25
return trip:
300/t2 = x+25 --> x = 300/t2 -25

setting the 2 equations equal and substituting
300/(5-t2) +25 = 300/t2 -25
300/t2 - 300/(5-t2) = 50
**for simplicity, i will just use t instead of t2 from now on**
[300(5-t) -300t]/t(5-t) = 50
1500-600t = 50t(5-t)
50t^2 -850t +1500 = 0
t^2 -17t +30 = 0
(t-15)(t-2) = 0
t = 2 or 15,
t2 can't be 15 because the total time is 5 hours

Therefore,
t1 = 3 hrs
t2 = 2 hrs
x = 125 mph

Answer 2

thanks!