Question

the distance between delhi and agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. how fast must the train travel the next 100 km, so as to average 70 km /h for the whole journey​

Answer 1

Also let the speed of the train while covering the second \[100km\] be \[S\] . Hence, the train needs to travel with a speed of \[116.66km/h\] during the second half of the travel to make the average speed of the train \[70km/h\] .

Answer 2

Given:-

• The distance between delhi and agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. how fast must the train travel the next 100 km, so as to average 70 km /h for the whole journey.

To Find:-

• How fast must the train travel the next 100 km, so as to average 70 km /h for the whole journey.

Solution:-

$t _1 = \frac{Distance}{Time} = \bigg( \frac{100}{50} \bigg) = 2hr$

Let Velocity in Next = $v_2$

Then,

$\green{⇝t_2 = \frac{100}{v_2} } \\ \\ \\ \\ \color{green}⇝Average \: Speed \: = \frac{Total \: Distance}{Total \: Time} \\ \\ \\ \\ \color{teal}⇝70 = \frac{200}{2 + \frac{100}{v_2} } \\ \\ \\ \\ \color{green} ⇝ 14 + \frac{700}{v_2} = 20 \\ \\ \\ \\ \green{⇝ \frac{700}{v_2} = 6 }\\ \\ \\ \\ \color{teal}⇝v_2 = \frac{700}{6} km/ h \\ \\ \\ \\ \color{lime}\boxed{ = 116 .66km/ \: h}$