Mike can travel 120 miles by car in the same amount of time

Mike can travel 120 miles by car in the same amount of time he can take the train 150 miles. if the train travels 10 miles faster than the car, find the speed of the car and the speed of the train.

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate (speed) of the car
Then r+10=rate of the train
Time travelling by car=120/r
Time travelling by train=150/(r+10)
Now we are told that the above two times are equal. so:
120/r=150/(r+10) multiply each term by r(r+10) (or cross multiply)
120(r+10)=150r get rid of parens (distributive law)
120r+1200=150r subtract 120r from each side
120r-120r+1200=150r-120r collect like terms
30r=1200 divide each side by 30
r=40 mph----------------------------speed of the car
r+10=40+10=50 mph--------------------speed of the train
CK
120/40=150/50
3=3