Question

A train 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?

Answer 1

Distance between B and C =
`3* 55=165miles`

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=Speed* Time`

∴ distance travelled between station A and B

=
`40* xmiles`

distance travelled between station B and station C

=
`55* ymiles`

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 =
`3* 55=165miles`