Question

Distance between Delhi and agra is 200 km A train travels first 100 kmat the speed of 50 km/hour how fast must the train travels by next 100 km so as the average speed 70 km/hour for whole journey.

Answer 1

Average speed=>>>
Vavg = 2v1v2/v1+v2
Vavg = 2× 70×50 /70+50 = 7000/120
Vavg. = 58.3 km/ hour

Answer 2

$average \: speed = \frac{total \: distance}{total \: time \: taken} \\ so \: according \: to \: question \\ total \: distance \: is \: given \: which \: is \: 200km \\ now \: what \: we \: have \: to \: find \: is \: total \: time \: so \: lets \: start$
100 km @ 50 km/hr

$so \: time \: taken \: for \: covering \: 100km \: is \\ \frac{distance}{speed} \\ \frac{100}{50} = 2hrs$
take time for next 100 km be x
$so \\ by \: formula \: of \: avg \: speed \\ avg \: speed = \frac{200}{2 + x} = 70 \\ 200 = 140 + 70x \\ 60 = 70x \\ x = \frac{60}{70} = \frac{6}{7} hrs$
$time \: taken \: for \: oter \: 100km \: is \: \frac{6}{7} hr \\ \\ now \: speed \: = \frac{distance}{time} \\ speed = \frac{100}{ \frac{6}{7} } \\ speed = \frac{700}{6} \frac{km}{hr}$

speed for next 100 km is 700/6 km/hr