Question

An athlete runs 30km at uniform speed of 30km/hr.how fast the athlete should run the next 90km. so as to average speed for entire journey 60km/hr

Answer 1

Hey friend
here is your answer
I case
distance = 30 km
speed =30 km/hr
so, time = 1 hr

II case
assuming the speed be "x" km/hr
distance =90 km
time =90/x


$average \: speed\: = \frac{total \: distance}{ \: total \: time} \\ 60= \frac{90 + 30}{1 + \frac{90}{x} } \\ 1 + \frac{90}{x} = \frac{120}{60} \\ 1 + \frac{90}{x} = 2 \\ \frac{90}{x} = 1 \\ x = 90km {hr}^{ - 1}$
so, the speed at II case must be 90 km/hr


glad to help you
hope it helps
thank you.