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nydimaria [60]
2 years ago
5

Traveling math word problem - thank you! :)

Mathematics
1 answer:
Anni [7]2 years ago
7 0

<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 \frac{miles}{hour} * (t+2) hours                             [distance = velocity * time]

d = 50(t+2) miles

rewriting in terms of t

t = \frac{d-100}{50}

<u>Distance travelled by the train:</u>

d = 70 \frac{miles}{hour} * t hours

d = 70t miles

rewriting in terms of t

t = \frac{d}{70}

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>t = \frac{d-100}{50}<u></u>

<u></u>t = \frac{d}{70}<u></u>

because t is the same:

\frac{d-100}{50} = \frac{d}{70}

\frac{d-100}{5} = \frac{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!

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