An airplane flew in a straight line into a headwind for 6 hours, covering 2,550 miles. It then flew in the exact opposite direction (with the headwind now a tailwind behind it) at the same engine speed for 3 hours, traveling an additional 1,725 miles. How fast would the plane have been flying (in mph) if there was no wind?
To solve this question lets see the concepts then solve it.
CONCEPTS:
1-Speed is the units of distance covered in a single unit of time.
2- Units of distance can be miles, kilometers, meters, light years etc.
3-We can use any distance unit and we can use any time units.
4-Here we are using miles per hour
5-Headwind means airplane and wind are moving against each other which means that they are moving in opposite directions tailwind means that airplane and wind are moving in the same direction.
6-Headwind reduces the speed and tailwind increases the speed.
7- It is assumed here that the speed of the wind is constant.
SOLUTION:
S=D/T
S=Speed.
D=Distance and
T=Time.
Speed=miles covered in one hour.
Distance covered in 6 hours against the wind is 2250 miles.
Distance covered in 3 hours against wind = 2550/2 =1275 miles.
Distance covered in the direction of the wind=1725 miles.
S=D/T
Total Distance covered in 6 hours=1275 +1725=3000 miles.
Effects of wind canceled out because the effects were opposite in direction.
T=6 hours
S=3000/6
S=500 mph.(Miles per hour).
The airplane would have been flying 500 mph if there was no wind. HAVE A GOOD DAY:-).