Question

Traveling math word problem - thank you! :)

Answer 1

350 miles

Explanation:

Let :

• time taken by train = t
• time taken by car = t + 2
• speed of car = 50 mph
• speed of train = 70 mph

Finding t

• The distance travelled by both the train and the car are equal
• Distance (train) = Distance (car)
• Speed (train) × Time (train) = Speed (car) × Time (car)
• (70)(t) = 50(t + 2)
• 70t = 50t + 100
• 20t = 100
• t = 5 hours

Substitute t in the equation formed for distance travelled by the train

• Distance (train) = 70t
• Distance (train) = 70(5)
• Distance (train) = 350 miles

The distance from the railroad station (Pasadena) to the state fair (Sacramento) is 350 miles

Answer 2

We are given:

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

Assuming variables and making equations!

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

Distance travelled by the car:

d = 50
`(miles)/(hour)` * (t+2) hours [distance = velocity * time]

d = 50(t+2) miles

rewriting in terms of t

`t = (d-100)/(50)`

Distance travelled by the train:

d = 70
`(miles)/(hour)` * t hours

d = 70t miles

rewriting in terms of t

`t = (d)/(70)`

now we have two expressions for t, both of which are equal because t is just the time taken by the train

Finding the distance:

`t = (d-100)/(50)`

`t = (d)/(70)`

because t is the same:

`(d-100)/(50) = (d)/(70)`

`(d-100)/(5) = (d)/(7)`

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!