at maximum speed an airplane can travel 2460 miles against the wind in 6 hours. The plane can go the same distance, but with the wind in 5 hours. What is the speed of the plane with no wind?

Now you are asking us exam questions. Ask for help and you will get it (if we can help). Ask for an answer to an exam question and probably no-one will reply.

Dear Allison Lee,

I think there is some information that is needed and it is not given to you... having to do with wind resistance, inertia, friction...

1. Can you just say, well, since it takes the plane 6 hours with a headwind and 5 hours with a tailwind, then it can fly the distance in 5.5 hours if there is no wind? If so, then your answer is 2460/5.5 = 447.3 mph.

2. Can you say, accurately, the same factor f will slow the plane with a headwind, and speed the plane in a tailwind? Then if S is the speed of the plane with no wind, you would get two equations:

headwind: S - f = 2460/6

tailwind: S + f = 2460/5. Then solving for S,

2S = 902

S = 451 mph.

As suggested you can find your homework answer if you do the work, your math book as hundreds of examples, work on several for a couple of hours, then work your question to a solution.

Consider this line of reasoning.

Against the wind, it takes 6 hours to go 2460 miles.  With the wind, the plane takes 5.5 hours to go 2460 miles.

Distance = (speed) * (time)

2 * 2460 = total distance or 4920 miles flown by plane in (how long?) 11.5 hours.

4920 miles / 11.5 hours = 427.8260869565217 miles / hour.

Did I eliminate the force of the wind as a factor or was it ever a factor in this particular problem ?

And this particular problem is at least a slightly tricky one.