SOLUTION: Suzette must commute a total of 34 miles to work. She first drives her car 10 miles to the train station and then rides the train the rest of the way to work. The average speed of

Question 427724: Suzette must commute a total of 34 miles to work. She first drives her car 10 miles to the train station and then rides the train the rest of the way to work. The average speed of the train is 15 mi/h faster than the average speed of Suzette's car.
a) Express the time Suzette spends driving and the time she spends on the train as rational expressions
b) It takes Suzette a total of 1 hour to get to work. Write and solve an equation to find the average speed of Suzette's car.
c) does Suzetter spend a greater amount of time driving or on the train? explain
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
If Suzette drives her car 10 miles to work, then her rate can be described as 10/Xmph to give us the amount of time she spends driving her car. The remaining 24 miles are taken by train, which is represented by the equation 24/(X+15)mph.
So ;
a) drive time=10/X mph and train time = 24/(X+15)mph
b) solving for X, we get :
10/X + 24/X+15 = 1
Multiply through by (X)(X+15), we get
10X+150+24X=X^2+15X
0 = X^2-19X-150
0 = (X-25)(X+6)
X = 25, -6
Ignoring our negative answer, Suzette's car speed is 25 mph, and the train goes 40 mph.
c)Whether Suzette spends more time in her car, or the train; She travels 10 miles at 25 mph, so she spends 10 X 60 /25 or 24 minutes by car. And she spends 24 X 60/40 or 36 minutes by train (1hour minus 24 minutes).
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