On a 60 km track, a train travels the first 30 km at a uniform speed of 30 km h-1. How fast must the train travel the next 30 km so as to average 40 km h-1 for the entire trip?

On a

60 km

track, a train travels the first

30 km

at a uniform speed of

30 {km h}^{- 1}

. The train must travel at a speed of

60 {km h}^{- 1}

for the next

30 km

so as to average

40 {km h}^{- 1}

for the entire trip.
Given, Total distance,

d = 60 km

, speed during the first

30 km

v_{1} = 30 {km h}^{- 1}

and the average speed is,

v_{av} = 40 {km h}^{- 1}

v_{av} = \frac{total distance}{total time}

v_{av} = \frac{total distance}{t_{1} + t_{2}}

, where

t_{1} = \frac{30}{30} = 1 h

If, the speed for the next

30 km

is,

v_{2}

then-

40 = \frac{60}{1 + \frac{30}{v_{2}}}

40

(

v_{2} + 30) = 60 v_{2}

Therefore,

v_{2} = 6

{km h}^{- 1} .

On a $60 km$ track, a train travels the first $30 km$ at a uniform speed of $30 {km h}^{- 1}$ . How fast must the train travel the next $30 km$ so as to average $40 {km h}^{- 1}$ for the entire trip?