Question

On a 60km track, a train travel the first 30km at a uniform speed of 30km/h. How fast must the train travel the next 30km so as to average 40km/h for the entire trip? 

Answer 1

Solution:-
Since we know that,
$average \: speed = \frac{total \: distance}{total \: time} \\ 40 = \frac{60}{time} \\ time = \frac{60}{40} = \frac{3}{2}hrs$

Distance travelled during fist time =30km
Speed=30km/h
So,
$time = \frac{distance}{speed} \\ = > \frac{30}{30} = 1$
So,time taken during first time=1 hours

Now,
Distance travelled second time=30km
Let the speed be x
So,
$time = \frac{30}{x}$
A/q
$\frac{3}{2} =1 + \frac{30}{x} \\ \frac{3}{2} - 1 = \frac{30}{x} \\ \frac{1}{2} = \frac{30}{x}$
$x = 60$
Hence,the train should travel need 30km at speed of 60km/h so that the average speed be 40km/h