<PRE><B>Question 417085</B>
Two trains, one 350 feet long, the other 450 feet long, on parallel tracks, can
 pass each other completely in 8 seconds when moving in opposite directions.
  When moving in the same direction, the faster train completely passes the slower one in 16 seconds.  Find the speed of the slower train
:
let f = speed of the faster train (in ft/sec)
let s = speed of the slower train
:
The total distance covered when trains pass each other: 450 + 350 = 800 ft
:
Two distance equations; dist = time * speed
:
opposite directions, 
8(f + s) = 800
simplify, divide by 8
f + s = 100
:
Same direction
16(f - s) = 800
Simplify, divide by 16
f - s = 50
:
Add these two simplified equations
f + s = 100
f - s = 50
--------------addition eliminates s find f
2f = 150
f = {{{150/2}}}
f = 75 ft/sec speed of the faster train
:
Find s using the equation f + s = 100
75 + s = 100
s = 100 - 75
s = 25 ft/sec is the speed of the slower train
Convert to mph
{{{(25*3600)/5280}}} = 17.045 mph is the slow train
:
:
Check solution in the original opposite direction equation
8(75 + 25) = 800</PRE>