Question

A bus travelling the first one third distance at speed of 10km/h the next one fourth at 20km/h and the remaining at 40km/h . What is the average speed of bus?

Answer 1

Let distance travelled by bus is (M) km.

A bus traveling the first, one-third distance at the speed of 10 km/hr.

=> $\dfrac{1}{3}$ of M (distance)

=> $\dfrac{M}{3}$

Time taken to cover M/3 distance in 10 km/hr

=> $\dfrac{M}{3\:\times \:10}$

=> $\dfrac{M}{30}$

Similarly,

Bus covers next one-fourth at 20 km/hr

=> $\dfrac{M}{20\:\times\:4}$

=> $\dfrac{M}{80}$

Now,

Remaining distance = M - $\dfrac{M}{3}$ - $\dfrac{M}{4}$

=> $\dfrac{12M\:-\:4M\:-\:3M}{12}$

=> $\dfrac{5M}{12}$

The bus travel remaining distance in 40 km/hr.

=> $\dfrac{5M}{12\:\times \:40}$

=> $\dfrac{5M}{480}$

=> $\dfrac{M}{96}$

Now,

$\bold{Average\:speed\:=\:\dfrac{Total\:distance \:covered}{Total\:time\:taken}}$

We have total distance = M

Total time = $\dfrac{M}{10}$ + $\dfrac{M}{20}$ + $\dfrac{M}{40}$

=> $\dfrac{16M\:+\:6M\:+\:5M}{480}$

=> $\dfrac{27M}{480}$

=> 0.05625 M

So,

Average speed = $\dfrac{M}{0.05625M}$

=> $\dfrac{1}{0.05625}$

=> 17.78 km/hr

=> 18 km/hr (approx.)

∴ Average speed of the bus is 18 km/hr.

Answer 2

Answer:

$\huge\red{\boxed{\bf{\ulcorner{\mid{\overline{\underline{Answer:-}}}}}\mid}}$

=> Let total distance be x

It covered =

x/3 at 10

x/3 at 20

x/3 at 60

Times taken respectively are { d / t } 

x / 30

x / 60

x / 180 respectively

total time = x/30 + x /60 + x/180

= 10x / 180

= x / 18

Average speed of bus (avg speed)

= total distance / total time

avg speed = x / {x/18}

So, average speed = 18 km / h