Question

A cao toqvers 30 km atauniform speed
Of cokm/h and the next 30 kmat
Uniform Speed of 20 km/h.
Find its average speed.​

Answer 1

Appropriate Question :

A car travels 30 km at the uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h. Find its average speed.

Answer :

26.66 km/h

Explication of steps :

We know that,

$\boxed { \sf { Average \: speed =\dfrac{ Total \: distance}{Total \: time } }}$

Calculating total distance :

→ Total distance = Distance from A to B + Distance from B to C

→ Total distance = 30 km + 30 km

→ Total distance = 60 km $\dots \mathfrak (1)$

Calculating total time :

→ Total time = Time taken to cover the distance from A to B + time taken to cover the distance from B to C

» Time taken to cover the distance from A to B :

$\boxed { \sf { Time = \dfrac{Distance}{Speed } }}$

• Distance from A to B = 30 km
• Speed from A to B = 40 km/h

$\longrightarrow \sf { Time (t_1) = \dfrac{30}{40} hr}$

$\longrightarrow \sf { Time (t_1)= \dfrac{3}{4} hr}$

» Time taken to cover the distance from B to C :

$\boxed { \sf { Time = \dfrac{Distance}{Speed } }}$

• Distance from B to C = 30 km
• Speed from B to C = 20 km/h

$\longrightarrow \sf { Time (t_2) = \dfrac{30}{20} hr}$

$\longrightarrow \sf { Time (t_2)= \dfrac{3}{2} hr}$

» Calculating total time :

$\longrightarrow \sf { Total \: time = t_1 + t_2}$

$\longrightarrow \sf { Total \: time = \dfrac{3}{4} hr + \dfrac{3}{2} hr}$

$\longrightarrow \sf { Total \: time = \dfrac{3 + 6}{4} hr}$

$\longrightarrow \sf { Total \: time = \dfrac{9}{4} hr \dots \mathfrak (2)}$

Substituting the values from equation (1) and equation (2) in the average speed formula.

$\boxed { \rm { Average \: speed =\dfrac{ Total \: distance}{Total \: time } }}$

$\longmapsto \rm { Average \: speed = 60 \div \dfrac{9}{4} km/h}$

$\longmapsto \rm { Average \: speed = 60 \times \dfrac{4}{9}km/h }$

$\longmapsto \rm { Average \: speed = \dfrac{60 \times 4}{9}km/h }$

$\longmapsto \rm { Average \: speed = \dfrac{60 \times 4}{9} km/h}$

$\longmapsto \rm { Average \: speed = \dfrac{240}{9} km/h}$

$\longmapsto \boxed{\rm { Average \: speed = 26.66 \: km/h}}$

Therefore, average speed is 26.66 km/h.