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SCSmith
05-09-2006, 10:52 PM
A plane travels 1200 miles against the jet stream, causing its airspeed to be decreased by 20 miles per hour. On the return flight, the plane travels with the jet stream so that its airspeed is increased by 20 miles per hour. If the total flight time of the round trip is 6 and 1/3 hours, what would be the plane's rate in still air?

1200/r-20 + 1200/r+20=19/3
LCM is 3(r-20)(r+20); so
3*1200(r+20) + 3*1200(r-20)=19(r-20)(r+20)
3600r+7200+3600r-7200=19(r[squared]-400)
7200r=?
I am stuck at this point.

Denis
05-10-2006, 01:12 AM
A plane travels 1200 miles against the jet stream, causing its airspeed to be decreased by 20 miles per hour. On the return flight, the plane travels with the jet stream so that its airspeed is increased by 20 miles per hour. If the total flight time of the round trip is 6 and 1/3 hours, what would be the plane's rate in still air?

1200/r-20 + 1200/r+20=19/3
LCM is 3(r-20)(r+20); so
3*1200(r+20) + 3*1200(r-20)=19(r-20)(r+20)
3600r+7200+3600r-7200=19(r[squared]-400)
7200r=?
I am stuck at this point.
You're complicating it, SC.

r = speed, t = time against wind; so time with wind = 19/3 - t

against wind: r - 10 = 1200 / t
with wind: r + 10 = 1200 / (19/3 - t)

Get both in terms of t, then solve for r.

Mrspi
05-10-2006, 09:31 AM
A plane travels 1200 miles against the jet stream, causing its airspeed to be decreased by 20 miles per hour. On the return flight, the plane travels with the jet stream so that its airspeed is increased by 20 miles per hour. If the total flight time of the round trip is 6 and 1/3 hours, what would be the plane's rate in still air?

1200/r-20 + 1200/r+20=19/3
LCM is 3(r-20)(r+20); so
3*1200(r+20) + 3*1200(r-20)=19(r-20)(r+20)
3600r+72000+3600r-72000=19(r[squared]-400)
7200r=?
I am stuck at this point.

I corrected a small multiplication error in your work (since the two quantities added up to 0, in this case, it didn't affect your final result.....but this won't always be true. Be careful with your multiplications!)

Ok....now you have
7200r = 19(r<sup>2</sup> - 400)

Do the multiplication on the right side:
7200r = 19r<sup>2</sup> - 7600

Subtract 7200r from both sides of the equation to get 0 on the left side (and arrange the right side in descending order):
0 = 19r<sup>2</sup> - 7200r - 7600

Rather than try to factor the right side, I would use the quadratic formula......

I hope this helps you.