Question 427724
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).