SOLUTION: 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 af

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.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
= 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
= 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

RELATED QUESTIONS
Two trains pass eachother in opposite directions. After 18 seconds they are 500m apart.... (answered by htmentor)

Thanks for your help. Shouldn't the 500 meters be converted to .5km and the 1000... (answered by Alan3354)

Two trains, one 500 meters long and the other 1000 meters long, are traveling in opposite (answered by khwang,ohthatstheanswer)

two trains start at the same spot and travel in opposite directions. one train travels 5... (answered by ewatrrr)

at 10:30am two cars pass each other as they travel in opposite directions along a... (answered by macston)

Two tankers, one 240 m in length and the other 180 m in length, travel parallel to each... (answered by ikleyn)

Two tankers, one 250 m in length and the other 110 m in length, travel parallel to each... (answered by ikleyn)

Help please! Two trains travel for eleven hours, starting from the same place traveling... (answered by nerdybill)

Two trains leave Cleveland at the same time. One train travels east and the other travels (answered by JulietG)