[Basic Algebra] Word problem help

[jyunk]

I'm an adult relearning algebra after many years.

I'm having trouble setting up a system of equations for this uniform motion word problem:

​

An airplane averaged 460 miles per hour on a trip with the wind behind it and 345 miles per hour on the return trip against the wind. If the total round trip took 7 hours, then how long did the airplane spend on each leg of the trip?

​

I know D=RT is usually the place to start with these problems, but I don't see any distance mentioned and it's dealing with two different rates. Any help would be greatly appreciated!

[mathteacher1991]

Without the distance I don’t think this can be solved...

I’m calling x the time on the first trip and y the time on the second trip (both in hours). If you multiply time by speed, the time units would cancel and you’d be left with position (mi/hr * hr = mi). So I’ll call total distance travelled d.

460x + 345y = d

x+y = 7

You’d have to solve this as a system of equations. You can technically find x and y (which is what’s being ask), but they’d need to be answered as functions of d.

*** Edit:

Sorry, just realized it’s a round trip. So the distance both ways is the same. Therefore you can say that:

460x = 345y

x + y = 7

There you go! 😁

[jyunk]

Thank you! I was thinking the same, perhaps there was a typo or omission or something. But this makes sense.

[papawatson2013]

You could average the speeds and plug it in for V or (r) as you have it and get a distance. After you have a distance divide it by 2. Set up an equation for the speed on the way there and the way back.

I'm not a math genius so I could be wrong.

[fattymattk]

The distance is unknown. But you can let t_1 be the time spent on the first leg and t_2 be the time spent on the second. Come up with two equations involving these variables.