SOLUTION: 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 d

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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 d      Log On


   

Question 65328: 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? Be sure to give the driving time for both days in the right hand column.
Note: I must use algebra for this problem!
Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
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.

Time for the trip on day 2 = x so the time on day 1 was x + 2
Speed = distance/time so
360%2F%28x%2B2%29=270%2Fx
Multiply each side by x
360x%2F%28x%2B2%29=270
Multiply each side by (x+2)
360x=270%28x%2B2%29
360x=270x%2B540%29
Subtract 270x from each side
90x=540%29
x=540/90
=6 hours and the day 1 time was 8 hours
(A non algebra method would take the idea that the extra 90 miles took 2 hours so her speed is 45 miles per hour. The times would therefore be 360/45 = 8 hours and 270/45=6 hours)