Question

a car travels X km at 60km per hr and then travels another 2x km at 40km/hr. find average speed for entire distance

Answer 1

total distance= 3x

time for first=x/60

time for second=2x/40

totaltime= x/60+2x/40 =8x/120

average speed= total distance/total time taken

                     =3x/8x * 120=90/2
                     =45 km/hr

Answer 2

Given:

A car travels x km at 60km per hr and then travels another 2x km at 40km/hr.

To find:

The average speed for the entire distance.

Solution:

As we know that when an object is moving at a speed 's' and covers distance 'd' in time 't' then its speed is given by:

$s = \frac{d}{t}$

So,

As given,

The speed of the car when it travels x km = 60 Km/hr.

So, the time that is taken by the car to travel x km

$= \frac{x}{60} \: hr$

Also,

the speed of the car when it travels 2x km = 40 Km/hr.

So, the time that is taken by the car to travel 2x km

$= \frac{2x}{40} \: km$

$= \frac{x}{20} \: km$

Hence,

the average speed for the entire distance

$= \frac{total \: distance \: travelled}{total \: time \: taken}$

$= \frac{x + 2x}{ \frac{x}{60} + \frac{x}{20} }$

On solving the above, we get

$= \frac{3x}{ \frac{x + 3x}{60} }$

$= \frac{3x}{ \frac{4x}{60} }$

$= \frac{3 \times 60}{4}$

$= 3 \times 15$

$= 45 \: km/hr$

Hence, the average speed for the entire distance is 45 km/hr.