Question

a body travels half journey with speed 10m/s and 1/3rd journey with a speed of 5m/s. remaining distance with a speed of 2m/s. find the average speed.​

Answer 1

Given,

Speed during the first half of the journey = 10m/s

Speed during 1/3rd of the journey = 5m/s

Speed during the rest of the journey = 2m/s

To Find,

The average speed during the journey.

Solution,

Let the total distance covered during the journey be D

Time taken for completing the first half of the journey;

= $\frac{distance}{speed}$

= $\frac{D}{2}$×$\frac{1}{10}$

=$\frac{D}{20}$ seconds

Time taken to complete the 1/3rd part of the journey :

= $\frac{distance}{speed}$

=$\frac{D}{3}$×$\frac{1}{5}$

=$\frac{D}{15}$ seconds

The distance left to cover :

=D- $\frac{D}{2}$-$\frac{D}{3}$

=$\frac{D}{6}$ m

Time taken to cover the 1/6th of the journey:

= $\frac{distance}{speed}$

=$\frac{D}{6}$ ×$\frac{1}{2}$

=$\frac{D}{12}$ seconds

The total time taken;

=$\frac{D}{15}$ +$\frac{D}{6}$ +$\frac{D}{12}$

=$\frac{19D}{60}$ seconds

The average speed of the journey :

=$\frac{Total distance}{Total time}$

=D×$\frac{60}{19D}$ m/s

= $\frac{60}{19}$ m/s

=3.15 m/s

Hence, the average speed of the journey is 3.15 m/s