Associated Topics || Dr. Math Home || Search Dr. Math

### Train, Distance, and Speed

```
Date: 09/20/97 at 12:01:04
From: jenny
Subject: Word problem, finding distances and speeds

Bobo is 1/3 of the way across a bridge when he hears a train whistle
behind him. A huge locomotive and tons of boxcars are coming at him at
45 mph.

Bobo knows that he can make it to the far edge of the bridge at the
exact same instant as the train, but he also knows that he can run
toward the train and reach the near end of the bridge just as the
train gets there. How fast does Bobo run?
```

```
Date: 09/20/97 at 12:50:44
From: Doctor Anthony
Subject: Re: Word problem, finding distances and speeds

Train ->45mph    A      u<- Bobo ->u                    B
|----------------||-----------|------------------------||
x             (1/3)L             (2/3)L

You must introduce letters to represent unknown quantities so you
can write down equations connecting times, distances, speeds etc.

The time for Bobo to reach end B of the bridge is (2/3)L/u

The time for the train to reach the same point B is (L+x)/45,
so we can equate these

(2/3)L     L + x
------  =  -----    ........(1)
u          45

Similarly, the time for Bobo reach A is (1/3)L/u and this equals the
time for the train to reach point A, x/45. Again equating these we get

(1/3)L      x
------  =  ---   ..........(2)
u        45

Now subtract equation(2) from equation(1)

(2/3)L-(1/3)L     L + x - x
-------------  = ----------
u              45

L       L
----  = ----
3u      45

and so  3u = 45   and u = 15 mph

Bobo can run at 15 mph.

An alternative and quicker method is to notice that Bobo has twice the
time to run to point B as he has to run to point A. So the relative
speed of Bobo and the train when Bobo runs towards the train is twice
the relative speed as when he runs away from the train.

This means   45 + u = 2(45 - u)

45 + u =  90 - 2u

3u = 45

u = 15  as before.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search