Atrain travels from station a to c having distance of 285 miles in 6 hours. during the journey, it reaches intermediate station b at the average speed of 40 miles/hr. from station b, train reaches station c at average speed of 55 miles/hr. what is the distance between the station b and c?

Distance between B and C =

Step-by-step explanation:

Let the time taken to reach from station A to B be x  hr

Let the time taken to reach from station B to C be y  hr

Given total time from station A to C be 6 hr

∴ x + y = 6

⇒ y = 6 - x → (1)

Also total distance given is 285 miles

As

∴ distance travelled between station A and B

  =

distance travelled between station B and station C

  =

So, 40x + 55y = 285  

⇒ 40x + 55(6 -x) = 285     (From 1)

=> 40x + 330 - 55x = 285

=> -15x = 285 - 330

=> -15x = -45  ⇒ x=3

gives y = 6-3 = 3 hours

Distance between B and C =