Relative velocity - find airspeed

[Delta G]

Homework Statement

A plane flies flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes 65 min less than the trip from A to B. What is the airspeed (assumed constant) of the plane?

a. 480 mi/h
c. 530 mi/h
b. 610 mi/h
d. 400 mi/h

Homework Equations

?

The Attempt at a Solution

65 min = 1.08 hrs
time from A to B = 2300 mi / 65 mi/hr = 35.4 hrs
time from B to A = 35.4 hrs - 1.08 hrs = 34.4 hrs

Not sure if I am doing it correctly and not sure where to go from here.

 

[kuruman]

First off, where did you get 2300 miles? No such number is mentioned in the problem statement. Secondly, even if you were told that the distance is 2300 miles, the plane cannot be flying at 65 mi/h if the headwind is also 65 mi/h because it would not move at all. Call the speed of the plane v and write two equations, one for the time A to B and one for the time B to A.

 

[kerimek]

To find the airspeed of the plane, we can use the formula:

Airspeed = (Distance traveled)/(Time taken)

We know that the distance traveled is the same for both trips, since it is a round trip. So, we can set the distances equal to each other:

2300 mi = 2300 mi

Next, we can set up equations for the time taken for each trip, using the given information:

Time from A to B = Distance/Airspeed + Time in headwind
Time from B to A = Distance/Airspeed - Time in headwind

Substituting in the given values, we get:

35.4 = 2300/Airspeed + 65
34.4 = 2300/Airspeed - 65

Solving for airspeed in both equations, we get:

Airspeed = 530 mi/h

Therefore, the correct answer is c. 530 mi/h.