Three railway stations, A, B, and C, are situated on a straight railway route. Station B is at 30 km in the east from station A and station C is at 60 km in east from station A. A train, with a constant average velocity, starts from A and reaches B in 15 minutes, and reaches C in 30 minutes. Assuming that station A is the origin, find the following: a. The position of the train moving from station A to station B after 10 minutes.
b. The position of the train moving from station A to station B after 10 minutes, if station B is assumed to be the origin.
c. The position of the train moving from station A to station B after 10 minutes, if station C is assumed to be the origin.

a.) 20 km east

b.) 50 km west

c.) 80 km west

Explanation:

As given,

Railway station -     A            B              C

Distance(km) -       0            30             60

Starts from A , train reaches B be in 15 minutes

Starts from A , train reaches C be in 30 minutes

a.)

If A is origin

As train covers 30km = 15 minutes

⇒ 15 minutes = 30 km

    1 minute = km

⇒ 10 minutes = 2×10 = 20 km

∴ we get

The position of the train moving from station A to station B after 10 minutes = 20 km east

b.)

If B is origin then , the position of  the train moving from station A to station B after 10 minutes = 30 + 20  = 50 km west

( Because B is the origin , so firstly train go from B to A in 15 minutes ( 30 km ) then A to B in 10 minutes (20 km) )

c.)

If C is the origin then , the position of  the train moving from station A to station B after 10 minutes = 60 + 20  = 80 km west

( Because C is the origin , so firstly train go from C to A in 30 minutes ( 60 km ) then A to B in 10 minutes (20 km) )