A person travels 285 km in 6 h. In the first part of the journey, he travels at 40 km/h by bus. In the second part, he travels at 55 km/h by train. what The distance travelled by train is?

Given data:

Total length of travelling (d) = 285 km

Speed of the bus (u) = 40 km/h

Speed of the train (v) = 55 km/h

Time of the travelling (t) = 6h

To find the expression of the distance travelled by the bus, write the equation of the speed of bus.

u=x/t'

Here, a x is the distance travelled by the bus and t' is the time of travelling by the bus.

Rearrange the above equation.

x=u × t'

Substitute 40 km/h for u in the above equation.

x=40t' ......(1)

Similarly, distance travelled by train can be expressed as,

y=55t".....(2)

Here, t" is the time of travelling by train.

Here, total distance can be expressed as,

d= x + y

Substitute 40t' for x, 55t" for y, and 285 km for d in the above equation.

285=40t' + 55t"  ......(3)

And total time of the journey can be expressed as,

t= t' + t"

Substitute 6 h for t in the above equation.

6=t' + t" ......(4)

Solving equation (3) and (4), we get,

t' = t" = 3 h

Substitute 3 h in the equation (2).

y=55(3)

y=165 km

Thus, the distance travelled by the train is 165 km.