Question

A train covers a distance of 20 km with a uniform speed of 60 km/h. It travels another distance of 40 km with a uniform speed of 80 km/h. Calculate the average speed of the train.

Answer 1

Given :

▪ A train covers a distance of 20km at a speed of 60kmph and another distance of 40km at a speed of 80kmph.

To Find :

▪ Average speed of the train.

Concept :

→ Average speed is defined as the ratio of total distance travelled to the total time taken.

→ It is a scalar quantity.

→ It has only magnitude.

→ It can't be negative or zero.

Calculation :

$\dashrightarrow\sf\:V_{av}=\dfrac{d_1+d_2}{t_1+t_2}\\ \\ \red{\dag\sf\:time(t)=\dfrac{distance}{speed}=\dfrac{d}{v}}\\ \\ \dashrightarrow\sf\:V_{av}=\dfrac{20+40}{\frac{20}{60}+\frac{40}{80}}\\ \\ \dashrightarrow\sf\:V_{av}=\dfrac{60}{\frac{1}{3}+\frac{1}{2}}\\ \\ \dashrightarrow\sf\:V_{av}=\dfrac{60\times 6}{5}=\dfrac{360}{5}\\ \\ \dashrightarrow\underline{\boxed{\bf{\purple{V_{av}=72kmph}}}}\:\gray{\bigstar}$

Answer 2

GIVEN:

• Speed of train when it covers a distance of 20km = 60 km/h
• Speed when it covers 40km = 80 km/h

TO FIND:

• Average speed

SOLUTION:

Time = Distance/Speed

Time ( t1 ) = 20/60

Time ( t1 ) = 1/3 h

__________________

Time ( t2 ) = 40/80

Time ( t2 ) = 1/2 h

Total time = t1 + t2

Total time = 1/2 + 1/3

Total time = 3 + 2/6

Total time = 5/6

Total distance = d1 + d2 = 20 + 40 = 60km

Avg speed = Total distance/Total time

Avg speed = 60/5/6

Avg speed = 360/5

Avg speed = 72km/h

Hence, Average speed = 72 km/h