Question 936907
Two trains pass each other in opposite directions.
 After 18 seconds the Locomotives are 500 m apart. 
 If they travel at the same speeds in the same direction, they are 50 m apart after 15 seconds.
 Find the speeds of the two trains in km per hour.
:
let a = speed of one train (meters/sec)
let b = speed of the other train
:
Write two distance equations, one for each way. dist = time * speed
:
18(a+b) = 500, going opposite directions, their speeds are additive
15(a-b) = 50, going the same direction, their speed are subtracted
:
18a + 18b = 500
15a - 15b = 50
:
multiply the first equation by 5, the 2nd equation by 6
90a + 90b = 2500
90a - 90b = 300
------------------Adding eliminates b, find a
180a = 2800
a = 2800/180
a = 15.555 m/sec
Convert to km/hr
{{{(3600*15.5555)/1000}}} = 56 km/hr, speed of train a
:
find b using the 1st equation
18(15.555) + 18b = 500
18b = 500 - 278
18b = 220
b = 220/18
b = 12.222 m/sec
convert to km/hr
{{{(3600*12.222)/1000}}} = 44 km/hr, speed of train b
:
;
Confirm this using these values (m/sec) in the 2nd equation
15(15.555) - 15(12.222) =
233.3 - 183.3 = 50 m