System of 2 linear equations?

Question

Against the wind a small plane flew 210 miles in 1 hour and ten minutes (70 minutes). The rturn trip tok only 50 minutes. What was the speed of the wind? What was the speed of the pane in still air?

x= wind speed y=plane speed in still air

I know that Distance=(rate)(time)

so..

210=(70)(y-x)
210=(50)(y+x)

210=70y - 70x
210=50y + 50x

1050=350y - 350x
1470=350y + 350x

2520=700y

y=3.6 mph..The book indicates that y should be 36mph..What did I do wrong?

Answer 1

You have mixed units. To solve, units must be consistent. Speed is in miles per hour so time must be in hours.

210=(70/60)(y-x)
210=(50/60)(y+x)

1260=7y - 7x
1260=5y + 5x

6300=35y - 35x
8820=35y + 35x

2520=70y

y = 36

Answer 2

Check your unit. Your speed is expressed in miles per HOUR.
You converted the time it traveled 1 hours and 10 minutes to MINUTES.

In order for your equations to work, the units must be the same.

Answer 3

You did the problem in minutes, and not hours. What you have is y = 2520 miles / 700 minutes = 3.6 miles / minute = 3.6 (miles / minute) (60 minutes / hour) = 3.6 (60) miles / hour = 216 miles / hour. Hmmm... Looks like something is really wrong!