Question

On a 100 km road, a car travels the first 50 km at a uniform speed of 30 km/hr^-1. How fast must the car travel for the next 50 km so as to have an average speed of 45 km/hr^-1 for the entire journey?

Answer 1

Answer:

90 km/hr fast must the car travel for the next 50 km

Explanation:

Given that,

Total distance = 100 km

First distance$d_{1} = 50\ km$

Speed$v_{1} = 30\ km/h^{-1}$

The car travels 50 km with speed 30 km/hr.

The time taken is

$t=\dfrac{d}{v}$

$t_{1}=\dfrac{50}{30}$

$t_{1}= 1.67\ hr$

Let us consider, the car travels next 50 km with speed v₂ km/hr.

The time taken is

$t_{2}= \dfrac{50}{v_{2}}$

The average speed $v_{avg}=\dfrac{D}{T}$  

Here, D = total distance

T= total time

The average speed is

$45=\dfrac{100}{\dfrac{5}{3}+\dfrac{50}{v_{2}}}$

$v_{2}=90\ km/hr$

Hence, 90 km/hr fast must the car travel for the next 50 km.

Answer 2

Answer:

Hence proved

Explanation:

my choice