Question

on a 100km track, a train travels the first 30 km at a uniform speed of 30 km/h. how fast must the train travel the next 70km so as to average 40 km/h for the entire trip​

Answer 1

$\large\bf\underline \blue{Given:-}$

• Track distance = 100km

• A train travelled the 1st 30km at a uniform speed = 30km/h

$\large\bf\underline \blue{To \: find:-}$

• how fast must the train travel the next 70km so as to average 40 km/h for the entire trip.

$\huge\bf\underline \red{Solution:-}$

$\small\bf \purple{Average \: Speed \: = \frac{Total \: distance \: travelled}{Total \: time \: taken} }$

• Time taken to cover 100km

$\longmapsto \rm \: t_1 = \frac{100}{40} \\ \\ \longmapsto \rm \: \frac{5}{2} \: hours \: \: \:$

When the train travelled with the speed of 30km/h then,

$\longmapsto \rm \: t_2 = \frac{30}{30} \\ \\ \longmapsto \rm1hour$

• For the remaining 70km

$\longmapsto \rm \:t_ 3 = t_ 1 - t_ 2 \\ \\\longmapsto \rm \:t_ 3 = \frac{5}{2} - 1 \\ \\ \longmapsto \rm \:t_ 3 = \frac{5 - 2}{2} \\ \\ \longmapsto \rm \:t_ 3 = \frac{3}{2} \: hours \\ \\ \bf \pink{ \: speed \: = \frac{distance}{time} } \\ \\ \longmapsto \rm \: speed = \frac{ \frac{70}{3} }{2} \\ \\ \longmapsto \rm \: speed = 70 \times \frac{2}{3} \\ \\ \longmapsto \rm \: speed = \frac{140}{3} \\ \\ \longmapsto \bf \red{ \: speed = 46.6km/h}$

So the train travel 70km with the speed of 46.6km/h .

Answer 2

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✰ Correct Question ✰

⋄ On a 100km track, a train travels the first 30 km at a uniform speed of 30 km/h. How fast must the train travel the next 70km as to average 40 km/h for the entire trip.

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✰ Given:-

⋄ Distance of track = 100km

⋄ Distance travelled by train first 30km at 30km/h.

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✰ To Find:-

⋄ How must fast the train travel the next 70 km so as the average speed is 40 km/h.

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✰ Solution :-

We know that,

➧ Av.Speed = TotalDistance / total time taken

⋄ Time taken by train to cover 100km.

➧ t = 100/40= 5/2h = 2.5h

⋄ For first the train cover 30km distance at rate of 30k/h.

∴ t' = 30/30= 1h.

and , for the remaining 70 km distance the time taken by train is

➧ t" = t-t'

➧ t"= 2.5h-1h

➧ t"= 1.5h.

∴ The time taken by train to cover 70km is 1.5h

Now,

➧ speed = distance /time

➧ speed = 70 /1.5

➧ speed = 46.6 km/h

∴ 70 km Distance covered by train at the speed of 46.6km/h.