Question

Two trains left the stations at the same time, moving towards each other. One train can cover the distance between the two train stations in 3 1/3 hours , the other covers the same distance in 2 4/5 hours. what portion of the distance between the two train stations is between the two trains in 2 hours after their departure?

Answer 1

hello

there are two trains i.e train A and train B

train A can travel from point x to point y in 3 1/3 hours

train B can travel cover that distance in 2 4/5 hours

let's convert the values from mixed fraction to improper fraction

`\begin{gathered} A=3(1)/(3)=(10)/(3)\text{hrs} \\ B=2(4)/(5)=(14)/(5)\text{hrs} \end{gathered}`

for train A, after 2 hour, the portion of the distance is

`\begin{gathered} x=(10)/(3)\text{hrs} \\ z=2\text{hrs} \\ 2x=(10)/(3)z \\ 6x=10z \\ z=(10)/(6)x \\ z=(5)/(3)x \end{gathered}`

for train A in two hours, the distance between it and the train station is 5/3 of the original distance

for train B, after 2 hours

`\begin{gathered} y=B=(14)/(5)\text{hrs} \\ y=(14)/(5)\text{hrs} \\ z=2\text{hrs} \\ 2y=(14)/(5)z \\ 14z=10y \\ z=(10)/(14)y \\ z=(5)/(7)y \end{gathered}`

after 2 hours, the distance B and the train station is 5/7 of the original distance