Help - Math word problems?

Question

Ariana took 2 hours longer to drive 360 miles on the first day of a trip than she took to drive 270 miles on the second day. If her speed was the same on both days, what was the driving time each day?


And this one as well :

A plane flies 720 miles against a steady 30 mi/hr headwind and then returns to the same point with the wind. If the entire trip takes 10 hours, what is the plane’s speed in still air?

Answer 1

First one is answered and correctly with 8 hours the first day and 6 hours the second (45 mi/hr if one cares).

Second one, one assumes the wind is the same either way so the time taken going is 720 mi / (speed - 30 mi/hr) and the time taken returning is 720 mi / (speed + 30 mi/hr). If you add those, they equal 10. Multiply each side by (speed - 30 mi/hr) and by (spedd + 30 mi/hr) which is speed^2 - 900 mi^2/hr^2. Clean up each side by adding/subtracting/etc., use "x" in place of "speed and you get 1440x = 10x^2 - 9000 and putting it into standard quadratic form, you get: 10x^2 - 1440x -9000. Solve with the quadratic formula and your answers are x = 150 and x = 0. Since speed in still air = 0 implies travelling at -30 mi/hr against the wind, we'll figure that one is utterly impractical which leaves speed in still air = 150 mi/hr as the answer. (Substitute back and you get 10. Always check!)

Answer 2

1) d=rt so r=d/t
r=360/(t+2)
r=270/t
360/(t+2)=270/t
270t+540=360t
540=90t
6=t
6+2=8
She drove for 8 hours the first day and 6 hours the second

2) The answer depends on how fast the wind was blowing on the trip back.

Answer 3

your equation is x (the amount it took to drive) +2/360 is to x/270

cross multiply to get the answer