Question 351120
A passenger on the front train A observes that he passes the complete length
 of train B in 33 seconds when traveling in the same direction as B and in
 3 seconds when traveling in the opposite direction.
 If B is 330 ft long, find the speed of the two trains.
:
Let a = train A's speed, Let b = train B's speed
:
When traveling in the same direction, their relative speed is (a-b)
When traveling in opposite direction, their relative speed is (a+b)
:
We will be finding the speeds in ft/sec
:
Write two distance equations, dist = speed * time
33(a-b) = 330
33a - 33b = 330
simplify, divide by 33
a - b = 10
and
3(a+b) = 330
3a + 3b = 330
simplify, divide by 3
a + b = 110
:
Use elimination on these two equations
a - b = 10
a + b = 110
-----------------adding eliminates b, find a
2a = 120
a = {{{120/2}}}
a = 60 ft/sec; speed of Train A; (that's {{{((60*3600))/5280}}} = 40.9 mph
and
a + b = 110
60 + b = 110
b = 110 - 60
b = 50 ft/sec; speed of Train B: (that's {{{((50*3600))/5280}}} = 34.1 mph