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?

Respuesta :

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

[tex]\begin{gathered} A=3\frac{1}{3}=\frac{10}{3}\text{hrs} \\ B=2\frac{4}{5}=\frac{14}{5}\text{hrs} \end{gathered}[/tex]

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

[tex]\begin{gathered} x=\frac{10}{3}\text{hrs} \\ z=2\text{hrs} \\ 2x=\frac{10}{3}z \\ 6x=10z \\ z=\frac{10}{6}x \\ z=\frac{5}{3}x \end{gathered}[/tex]

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

[tex]\begin{gathered} y=B=\frac{14}{5}\text{hrs} \\ y=\frac{14}{5}\text{hrs} \\ z=2\text{hrs} \\ 2y=\frac{14}{5}z \\ 14z=10y \\ z=\frac{10}{14}y \\ z=\frac{5}{7}y \end{gathered}[/tex]

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