Question

3. A dog ran at 30 km/h for 40 minutes and then returned to the starting point at 20 km/h.
Find its average speed.​

Answer 1

AnswEr :

The average speed of the dog is

24km/h

ExplanaTion :

Given :

• Dog ran with 30km/h speed for 40min and reached its destination of distance d

• It returned back with 20km/h speed in time t and distance d.

Solution :

In case (1)

Speed of dog = 30km/h

Time Taken by it = 40 min = 40/60 hrs = 2/3hrs

=> Time = 2/3 hrs

we know that,

distance = speed × time

by using this formula,

distance covered by the dog = 30 × 2/3

=> distance = 20km.

In case (2)

speed of dog = 20km/h

distance = 20km

we know that,

time = speed / distance covered .

so, here

time = 20/20 hrs

=> time = 1 hr.

According to the question,

$avg.speed \: = \frac{total \: distance}{total \: time \: taken}$

$\implies \: avg.speed \: = \frac{(d1 + d2)}{(t1 + t2)}$

$\implies \: avg.speed \: = \frac{(20 + 20)}{( \frac{2}{3} + 1) }$

$\implies \: avg.speed \: = \frac{40}{ \frac{5}{3} }$

$\implies \: avg.speed \: = \frac{(40 \times 3)}{5}$

$\implies \: avg.speed \: = \cancel \frac{40}{5} \times 3$

$\implies \: avg.speed \: = (8 \times 3)$

$\implies \: avg.speed \: = 24kmph$

Therefore, the average speed of the dog is 24kmph or 24km/h

Answer 2

ANSWER:

Given

• Dog ran at 30km/h for 40 min

Case ( 1 )

• It returned with speed of 20km/h

Case ( 2 )

TO FIND:

Average speed of Dog

Let the returned time & distance be 't' & 'd'

In case ( 1 )

Speed of dog = 30km/h

Time taken by dog = 40

40 → Hours

= 40/60

Time(t1) = 2/3 hrs

Note : I've converted 40 min → Hours because the speed is in km/h

Using

Distance(d) = speed(s) × time(t)

Distance(d) = 30 × 2/3

→ Distance(d1) = 20 km

In case ( 2 )

Speed of dog = 20km/h

Here,

Distance(d2) covered in 1hr = 20km

→ Time(t2) = 1hr

$\to \small{ \sf{ speed_{avg} = \dfrac{ d_{1} + d_{2} }{ t_{1} + t_{2} } }} \\ \to \small{ \sf{ speed_{avg} = \dfrac{20 +20 }{ \frac{2}{3} + 1} }} \\ \to \small{ \sf{ speed_{avg} = \dfrac{ 40 }{ \frac{ 5}{ 3} } = 8 \times 3}}$

Average speed of Dog = 24km/g