A train travels 40 km at a uniform speed of $30 k m h^{- 1}$ . Its average speed after travelling another 40 km is $45 k m h^{- 1}$ for the whole journey. Its average speed and the speed in the second half of the journey is

A v e r a g e s p e e d = 45 k m h^{- 1}

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S p e e d i n t h e s e c o n d h a l f o f t h e j o u r n e y = 90 k m h^{- 1}

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A v e r a g e s p e e d = 60 k m h^{- 1}

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S p e e d i n t h e s e c o n d h a l f o f t h e j o u r n e y = 110 k m h^{- 1}

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Solution

The correct options are
A $A v e r a g e s p e e d = 45 k m h^{- 1}$
B $S p e e d i n t h e s e c o n d h a l f o f t h e j o u r n e y = 90 k m h^{- 1}$
Let speed of the train in later half = x, then the time taken to travel later 40 km = 40/x hours
Total time taken $= \frac{40}{30} + \frac{40}{x}$
Average speed = $\frac{T o t a l d i s t a n c e}{T o t a l t i m e} = 45$
$\frac{80}{\frac{40}{30} + \frac{40}{x}} = 45$
$4 x + 120 = \frac{80}{45} \times 3 x$
$x = 90 k m h^{- 1}$

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Similar questions

A train travels 40 km at a uniform speed of $30 k m h^{- 1}$ . Its average speed for the whole journey after travelling another 40 km is $45 k m h^{- 1}$ . Its speed in the second half of the journey is ____.

Q. On a 100 km road, a car travels the first 50 km at a uniform speed of

30 k m h^{- 1}

. Assuming constant velocity in second half also, how fast must the car travel for the next 50 km so as to have an average speed of

45 k m h^{- 1}

for the entire journey?

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A train travels 40 km at a uniform speed of 30kmh−1. Its average speed after travelling another 40 km is 45kmh−1 for the whole journey. Its average speed and the speed in the second half of the journey is

A train travels 40 km at a uniform speed of $30 k m h^{- 1}$ . Its average speed after travelling another 40 km is $45 k m h^{- 1}$ for the whole journey. Its average speed and the speed in the second half of the journey is