An airplane flying into a headwind travels 1128.00 miles in 4 hours and 42 minutes.On the return flight,the distance is traveled in 4 hours.Find the airspeed of the plane and the speed of the wind,assuming that both remain constant.
A)plane speed = 238 mph;wind speed = 250 mph
B)plane speed = 276 mph;wind speed = 21.00 mph
C)plane speed = 261.00 mph;wind speed = 21.00 mph
D)plane speed = 238 mph;wind speed = 21.00 mph
E)plane speed = 276 mph;wind speed = 268 mph

Question

An airplane flying into a headwind travels 1128.00 miles in 4 hours and 42 minutes.On the return flight,the distance is traveled in 4 hours.Find the airspeed of the plane and the speed of the wind,assuming that both remain constant. ​
A)plane speed = 238 mph;wind speed = 250 mph
B)plane speed = 276 mph;wind speed = 21.00 mph
C)plane speed = 261.00 mph;wind speed = 21.00 mph
D)plane speed = 238 mph;wind speed = 21.00 mph
E)plane speed = 276 mph;wind speed = 268 mph

Quizplus · Accepted Answer

Let's denote the airspeed of the plane as x and the speed of the wind as y.

From the first leg of the trip, we can set up the equation:

x - y = 1128/4.7

Simplifying, we get:

x - y = 240

From the second leg of the trip, we can set up another equation:

x + y = 1128/4

Simplifying, we get:

x + y = 282

Now we have a system of two equations with two variables, which we can solve for x and y. One way to do this is to add the two equations together:

2x = 522

x = 261

Substituting this value of x back into one of the equations, we can solve for y:

261 + y = 282

y = 21

Therefore, the airspeed of the plane is 261 mph and the speed of the wind is 21 mph. The correct answer is C.

An Airplane Flying into a Headwind Travels 1128