Question

On a 200 km track, a train travels the first 50 km at a uniform speed of 40 km/h. How fast train must travel the next 150km so as to maintain the average speed of 60 km/h for the whole journey?

Answer 1

Let the total time taken be x.
$average \: speed = \frac{total \: distance}{total \: time \: taken}$
$60 = \frac{200}{x}$
$x = \frac{200}{60} = \frac{10}{3}$
D1=50m
S1 =40 km/h
T1 =?

D2=150km
S2 =?
T2=?

Since we know that,
$speed = \frac{distance}{time}$
so,
$time = \frac{distance}{speed}$
$t 1 = \frac{d1}{s1} = \frac{50}{40} = \frac{5}{4}$
And,
Similarly..
$t2 = \frac{d2}{s2} = \frac{150}{s2}$
Now,
A/q
$\frac{5}{4} + \frac{150}{s2} = \frac{10}{3}$
$\frac{150}{s2} = \frac{10}{3} - \frac{5}{4} \\ \frac{150}{s2} = \frac{40 - 15}{12} = \frac{25}{12}$
$s2 = \frac{12 \times 150}{25}$
s2=72km/h