Question

On a 120 km track A train travels the first 30 km at a speed of 30 km per hour how fast must the train travel the next 90 km so as to get average speed of 60 km per hour for the entire trip

Answer 1

Given : -

•A track is 120km and a train travels the first 30km at a speed of 30km/ hr.

•The train travels the next 90km at a speed of 60km/hr.

To Find : -

•Find the time travel by train.

Solution : -

$\: \sf \: total \: distance \: to \: be \: travelled = (30 + 90)km = 120km$

Now,

Let consider the speed of the train be u km/hr for next 90 km.Then the time taken to cover 90km with speed u km/hr,

$\: \sf \: t1 = \frac{90}{u} hr$

Time taken to cover first 30km with the speed of 30km/hr,

$\: \sf \: t2 = \frac{30}{30} = 1hr$

So,

$\: \sf \: total \: time = t1 + t2 = ( \frac{90}{u} + 1)$

we have,

$\: \sf \large \implies \: average \: speed \: = \frac{total \: distance}{total \: time}$

Now substitute the values

$\: \sf \implies \: 60 \frac{km}{hr} = \frac{120km}{ (\frac{90}{u} + 1) hr } \\ \\ \: \sf \implies \: 60 = \frac{120}{ \frac{90 + u}{u} } \\ \\ \: \sf \implies \: 90 + u = ( \frac{120}{60} ) \times u \\ \\ \: \sf \implies \: 90 + u - 2u = 0 \\ \\ \: \sf \implies \: 2u - u = 90 \\ \\ \: \sf \implies \: u = 90 \frac{km}{hr}$

Hence,average speed of train is 90km/hr

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