Word problem: A Train

[silverdragon316]

A Train leaves Martinsville and travels south at a speed of 75 mph. One Hour later, a second trains leaves on a parallel track and travels south at 90mph. How far from the station will the second train over take the first train?


I calculated 376 miles. I figured the train has 75 miles to catch up. Since the second train makes a gain of 15 mph every hour it would take 5 hours to make up 75 miles. 5 times 90 is 450 which is when the two trains would be even. I think the second train would over take the first train at 451 miles. If this is correct how would I have put this into a math formula? :?

 

[jwpaine]

90(x) = 75(x) + 75

x = 5 hours for train B to meet train A

You be the judge of how soon after the second passes it. Speed is still a factor. How far after do you want it to pass by? 1 foot, or 1 mile past?

Good problem solving.

 

[soroban]

Hello, silverdragon316!

You're reading stuff into the problem.
. . "Overtake" means "catch up" . . . not "pass".
[Besides, if it meant "pass", we'd have to know how long each train is, right?]

A train leaves Martinsville and travels south at a speed of 75 mph.
One hour later, a second trains leaves on a parallel track and travels south at 90 mph.
How far from the station will the second train over take the first train?

Your approach is a good one.
Train \(\displaystyle A\) has a one-hour headstart.
. . At 75 mph, it is already 75 miles ahead of train \(\displaystyle B.\)

Train \(\displaystyle B\) goes 90 mph, 15 mph faster than train \(\displaystyle A.\)
. . Train \(\displaystyle B\) gains 15 miles ever hour.
(It is as if train \(\displaystyle A\) has stopped and train \(\displaystyle B\) is approaching at 15 mph.)
. . To catch up 75 miles, it will take \(\displaystyle \frac{75}{15}\:=\:5\) hours.

They will both be \(\displaystyle 450\) miles from the station.

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If you need an equation, jwpaine gave you one . . .

Train \(\displaystyle A\) goes 75 miles first.
. . During the next \(\displaystyle t\) hours, it goes \(\displaystyle 75t\) miles.
Train \(\displaystyle A\) goes a total of: \(\displaystyle 75\,+\,75t\) miles.

Train \(\displaystyle B\) goes 90 mph.
. . During the same \(\displaystyle t\) hours, it goes \(\displaystyle 90t\) miles.

Since their distances are equal: \(\displaystyle \L\:75\,+\,75t\:=\:90t\)