Question

X2. A bus travelling the first one third distance at a speed of 10
km/h, the next one third at 20 km/h and the last one-third at
60 km/h. The average speed of the bus is
(a) 9km/h (b) 16 km/h (©) 18 kmh (d) 48 km/h
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Answer 1

Answer:-

Av = 18 km/hr

Option → C

Given :-

Distance covered at 10km/hr is 1/3

next one 20km/hr is 1/3, last one is 1/3 at 60 km/hr.

To find :-

The average speed of bus.

Solution:-

Average speed :- It is the ratio of the total distance covered by the body to the total time taken during its whole journey.

Let the distance cover by bus be s.

then,

s/3 at 10 km/hr

s/3 at 20km/hr

s/3 at 60 km/hr

★ $\boxed{\sf{T = \dfrac{s}{v}}}$

→$T_1 = \dfrac{\dfrac{s}{3}}{10}$

→$T_1 = \dfrac{s}{30}$

__________________________________________

→$T_2 = \dfrac{\dfrac{s}{3}}{20}$

→$T_2 = \dfrac{s}{60}$

__________________________________________

→$T_3 = \dfrac{\dfrac{s}{3}}{60}$

→$T_3 = \dfrac{s}{180}$

Total time taken = $T_1 + T_2 + T_3$

→$\dfrac{s}{30}+\dfrac{s}{60}+\dfrac{s}{180}$

→$\dfrac{6s + 3s + s }{180}$

→$\dfrac{10s}{180}$

→$\dfrac{s}{18}$

Average speed is given by :-

★ $\boxed{\sf{A_v = \dfrac {Total distance covered }{Total time taken }}}$

→$A_v = \dfrac{s}{\dfrac{s}{18}}$

→$A_v = \dfrac{18s}{s}$

→$A_v = 18 km/hr$

hence,

Average speed of bus will be 18 km/hr.

Answer 2

Answer:

Average speed of the bus= 18 km/h

Explanation:

let the total distance travelled by the bus be d

given that,

bus travelling the first one third distance at a speed of 10 km/h,

so,

distance travelled at speed 10 km/h =

d/3

time taken

= distance travelled/speed

= (d/3)/10

= d/30 h

also,

one third at 20 km/h

so,

here,

tine taken = (d/3)/20

= d/60 h

also,

last one third at 60 km/h

here,

time taken = (d/3)/60

= d/180

now,

Average speed =

total distance covered/total time taken

total distance covered = d

total time taken =

d/30 + d/60 + d/180

= (6d + 3d + d)/180

= 10d/180

= d/18

now,

Average speed =

d/(d/18)

= 18d/d

= 18 km/h

so,

Average speed of the bus

= 18 km/h