Question

the distance between Delhi and Agra is 200 km . A train travels the first 200 km at a speed of 100 km/h . How fast must the train travel the next 100km, so as to average 70km/h for the whole journey​

Answer 1

Answer:

200/100 +100/x =300/70

Time equal

2+100/x=30/7

100/x=30/7-2

100/x=16/7

x=7*100/16

x=7*6.25

x=43.75 km

Answer 2

$\sf\small\underline\red</p><p>{Given:-}$

Distance = 100 km

Speed = 50 km/h

$\sf\small\underline\red</p><p>{To \: \: Find:-}$

To find the average speed we need to use the relation:

$\sf\small\underline\red</p><p>{using \: formula:-}$

Average speed = Total distance traveled/ Total time taken

$\sf\small\underline\red</p><p>{Solution:-}</p><p>$

Let's find the time taken by train to travel each part of the distance.

For the first part:

Distance = 100 km

Speed = 50 km/h

Time = Distance/Speed = 100/50 = 2 h

For the second part:

Let the speed of the train be 's' km/h

Distance = 100 km

Time = Distance/Speed = 100/s

Now, as we know that:

Average speed = Total distance traveled/ Total time taken

where, Average speed = 70 km/h

Total distance travelled = 200 km

Total time taken = 2 + 100/s

Substituting these values in the average speed equation, we get:

Average speed = Total distance traveled/ Total time taken

or, 70 = 200/ (2 + 100/s)

or, 70 × (2 + 100/s) = 200

or, 140 + 7000/s = 200

or, 7000/s = 60

or, s = 7000/60

$= 116.67 \: km.h</p><p>$

$\sf\small\underline\red</p><p>{Note:-}</p><p>$

• Therefore, the speed of the train must be 116.67 km/h.

$\huge\mathtt{\fcolorbox{black}{black}{\orange{☯︎Good luck}☯︎}}</p><p></p><p>$