SOLUTION: In going over 750 kms, it takes a passenger plane 2 hour less time to fly with a tailwind of 50 kph than against a headwind travelling at the same speed. How fast was the passenger
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Question 1192602: In going over 750 kms, it takes a passenger plane 2 hour less time to fly with a tailwind of 50 kph than against a headwind travelling at the same speed. How fast was the passenger plane flying at each way of the course? Found 2 solutions by math_helper, greenestamps:Answer by math_helper(2461) (Show Source):
With the tailwind: (1)
With the headwind: (2)
Also, from the problem statement: or (3) (4)
With this information, you can write an equation with one unknown. I chose to write it with just but other elimination possibilities exist:
Multiply both sides by :
Simplify...
Factor:
This has solutions and
Take just the positive time solution --(by 3)-->
Now, km/hr km/hr
Check: --> (ok)
With the wording exactly as shown, the problem can't be answered, because we don't know the exact distance. (The problem says the plane went OVER 750km; it doesn't say it went 750km.)
Assuming the distance is in fact exactly 750km....
The plane's speed one direction is its speed in still air plus the wind speed; in the other direction it is its speed in still air minus the wind speed. Since the wind speed is 50km/h, the difference in the two speeds is 100km/h.
If a formal algebraic solution is not required, the problem can be solved quickly by playing with numbers. 150*5=750, and 250*3=750; so 5 hours at 150km/h and 3 hours at 250km/h satisfy the given conditions.
For a solution using formal algebra, I would let the two times in hours be x and x+2, so that the two speeds are 750/x and 750/(x+2). Then I would write and solve an equation that says the difference in speeds at the two times is 100km/h -- literally, "the speed for the shorter time is 100km/h more than the speed for the longer time":
or
The negative value for time of course makes no sense; so x=3 and x+2=5.
The two speeds are then 750/3=250 and 750/5=150.
ANSWERS: 250km/h with the wind; 150km/h against the wind
