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

Question 79595: 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?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d) = rate(r) times time(t) or d=rt, t=d/r and r=d/t
We are told that the speed (rate) on both days are the same
Let t=driving time on the second day of trip
Then t+2=driving time on first day of trip
Rate on second day=270/t
Rate on first day=360/(t+2)
But we are told that:
Rate on second day=rate on first day, so
270/t=360/(t+2) multiply both sides by t(t+2) to get rid of fractions
(270(t)(t+2))/t=(360(t)(t+2))/(t+2) simplify
270(t+2)=360t get rid of parens
270t+540=360t subtract 270t from both sides
360t-270t=270t-270t+540 collect like terms
90t=540 divide both sides by 90
t=6 hours-------------------driving time second day
t+2=6+2=8 hours----------------------driving time first day
ck
r=d/t
r=360/(6+2)=360/8=45 mph
r=270/6=45 mph

Hope this helps-----ptaylor

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