SOLUTION: A freight train left Seoul and traveled east at an average speed of 55 mph. A diesel train left one hour later and traveled in the same direction but with an average speed of 60 mp

Algebra.Com
Question 1122718: A freight train left Seoul and traveled east at an average speed of 55 mph. A diesel train left one hour later and traveled in the same direction but with an average speed of 60 mph. How long did the freight train travel before the diesel train caught up?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Notice that when the diesel train started, the freight train was 55 miles ahead.


But the diesel train, having the speed in 5 = 60-55 miles per hour greater than the freight train, 
    will decrease the distance between them by 5 miles each hour. 


So, it will take 11 hours  ( where   ) for the diesel train to catch the freight train.


Correspondingly, it will take 12 = 11+1 hours for the freight train to get the meeting point.


It is how the physicists solve such problem.

Below find the way on how this problem is solved in Algebra. 


Let t = "How long did the freight train travel before the diesel train caught up",  in hours  (the value under the question).


Then the diesel train traveled (t-1) hour.


They both covered the same distance:


    60*(t-1) = 55*t


    60t - 60 = 55t 


    60t - 55t = 60  ====>  t =  = 12 hours.

Solved   (in two different ways).

--------------------

See introductory lessons on Travel and Distance problems
    - Travel and Distance problems
    - Travel and Distance problems for two bodies moving in opposite directions
    - Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.

They are written specially for you.

You will find the solutions of many similar problems there.

Read them and learn once for all from these lessons on how to solve simple Travel and Distance problems.

Become an expert in this area.


Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
A freight train left Seoul and traveled east at an average speed of 55 mph. A diesel train left one hour later and traveled in the same direction but with an average speed of 60 mph. How long did the freight train travel before the diesel train caught up?
Let time freight train took to get to meeting point be T

Then time diesel train took to get to meeting point = T – 1

We then get the following DISTANCE equation: 55T = 60(T – 1)        OR          5(11T) = 5(12)(T - 1)

                                             55T = 60T – 60         OR          11T = 12T - 12

                                             55T – 60T = - 60       OR          11T - 12T = - 12 

                                            – 5T = - 60             OR          - T = - 12

T, or time freight train took to get to meeting point =  

RELATED QUESTIONS


A diesel train left Miami and traveled toward Johannesburg at an average speed of 10 mph.  (answered by richwmiller,josmiceli)

A train left the alabama and traveled east at an average speed of 12 mph.  An boat left... (answered by rfer)

 A diesel train left Washington and traveled
toward Johannesburg at an average speed of
 (answered by ankor@dixie-net.com)

A diesel train left berlin and traveled nort at an average speed of 20 mph. A freight... (answered by JulietG)

A cattle train left the station and traveled east at an average speed of 25k/h. Sometime... (answered by ikleyn)

A freight train left the station and traveled north at an average speed of 28.6 mph. A... (answered by ewatrrr)

Help me solve this word problem please. "A freight train and a diesel train left at the... (answered by rfer)

A cattle train left miami and traveled toward New York. 14 hours later a diesel train... (answered by ankor@dixie-net.com)

A cattle train left Miami and traveled toward new York. 14 hours later a diesel train... (answered by checkley77)