SOLUTION: Solve. 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

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Question 116877: Solve.
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?

Solve.
A plane flies 720 miles against a steady 30 mile per hour headwind and than 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 by ankor@dixie-net.com(22740) About Me  (Show Source):
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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?
:
Let t = time to drive 270 mi
then
(t+2) = time to drive 360 mi
:
Speed of the two days is given as equal, so write speed equation:
Speed = distance/time
:
360%2F%28%28t%2B2%29%29 = 270%2Ft
:
Cross multiply:
360t = 270(t+2)
:
360t = 270t + 540
:
360t - 270t = 540
:
90t = 540
:
t = 540/90
:
t = 6 hrs for the 270 mi day
then
6 + 2 = 8 hrs for the 360 mi day
:
Check solution by finding if the speeds, are indeed equal:
360/8 = 45 mph
270/6 = 45 mph, confirms our solution
:
:
Solve.
A plane flies 720 miles against a steady 30 mile per hour headwind and than
returns to the same point with the wind. If the entire trip takes 10 hours,
what is the plane's speed in still air?
:
Let s = speed in still air
Then
(s+30) = speed with the wind
and
(s-30) = speed against the wind
:
Write a time equation; Time = Distance/speed
:
With wind time + against wind time = 10 hrs
720%2F%28%28s%2B30%29%29 + 720%2F%28%28s-30%29%29 = 10
:
Multiply equation by (s+30)(s-30) to eliminate the denominators:
720(s-30) + 720(s+30) = 10(s-30)(s+30)
:
720s - 21600 + 720s + 21600 = 10(s^2 - 900)
:
1440s = 10s^2 - 9000
:
0 = 10s^2 - 1440s - 900; a quadratic equation:
:
Simplify, divide equation 10
s^2 - 144s - 900 = 0
:
Fortunately this will factor:
(s-150)(s+6) = 0
:
s = +150 mph (the only solution that makes sense) in still air
:
:
Check solution by finding the times.
with speed = 180; against speed = 120
:
720/120 = 6 hrs
720/180 = 4 hrs
---------------
Total hrs:10 hrs, confirms our solution
: