<u>We are given:</u>
car and train leave at the same time
average velocity of car = 50 miles/hour
average velocity of train = 70 miles/hour
train arrives 2 hours early
<u>Assuming variables and making equations!</u>
let the time taken by the train = t hours
since the car arrived late, it took more time as compared to the train
time taken by the car = t + 2 hours
since the distance from Pasadena to Sacramento doesn't change, both the vehicles covered the same distance, d
<u>Distance travelled by the car:</u>
d = 50 * (t+2) hours [distance = velocity * time]
d = 50(t+2) miles
rewriting in terms of t
<u>Distance travelled by the train:</u>
d = 70 * t hours
d = 70t miles
rewriting in terms of t
now we have two expressions for t, both of which are equal because t is just the time taken by the train
<u>Finding the distance:</u>
<u></u><u></u>
<u></u><u></u>
because t is the same:
7(d - 100) = 5(d)
7d - 700 = 5d
(7d - 5d) - 700 = 0 [subtracting 5d from both sides]
2d = 700 [adding 700 on both sides]
d = 350 miles [dividing both sides by 2]
The distance between Pasadena and Sacramento is 350 miles!