Question

A man travels 800 km by train at 80 km/hr, 420 km by car at 60 km/hr and 200 km by cycle at 20 km/hr. What is the average speed of the journey? Solution:​

Answer 1

Answer:

59.59 km/h

Explanation:

As per the provided information in the given question, we have :

• A man travels 800 km by train at 80 km/hr, 420 km by car at 60 km/hr and 200 km by cycle at 20 km/hr.

We've been asked to calculate average speed of the journey.

In order to calculate the average speed of the journey, we need to find the total distance travelled and total time taken. Let us say,

• S₁ = 800 km
• S₂ = 420 km
• S₃ = 200 km
• V₁ = 80 km/h
• V₂ = 60 km/h
• V₃ = 20 km/h

Also,

• T₁ = Time taken to cover 800 km by train
• T₂ = Time taken to cover 420 km by car
• T₃ = Time taken to cover 200 km by cycle

$\large {\underline { \sf {Total \; Distance \; Travelled :}}}$

$\dashrightarrow \quad \rm { S_{(Total)} = S_1 + S_2 + S_3}$

$\dashrightarrow \quad \rm { S_{(Total)} = (800 + 420+200) \; km}$

$\dashrightarrow \quad\underline{\boxed{ \rm { S_{(Total)} = 1420 \; km}}}$

$\rule{200}2$

$\large {\underline { \sf {Total \; Time \; Taken :}}}$

$\dashrightarrow \quad \rm { T_{(Total)} = T_1 + T_2 + T_3}$

• Time = Distance ÷ Speed

$\dashrightarrow \quad \rm { T_{(Total)} = \dfrac{S_1}{V_1} + \dfrac{S_2}{V_2} + \dfrac{S_3}{V_3}}$

$\dashrightarrow \quad \rm { T_{(Total)} = \Bigg (\cancel{ \dfrac{800}{80} }+ \cancel{\dfrac{420}{60}} +\cancel{ \dfrac{200}{20}} \Bigg ) \; h}$

$\dashrightarrow \quad \rm { T_{(Total)} = \Bigg ( 10 + 7 + 10 \Bigg ) \; h}$

$\dashrightarrow \quad\underline{\boxed{ \rm { T_{(Total)} = 27 \; h}}}$

$\rule{200}2$

$\large {\underline { \sf {Average \; Speed :}}}$

As we know that,

$\bigstar \quad \underline{\boxed {\bf { Speed_{(Avg)} = \dfrac{Distance_{(Total)} }{Time_{(Total)}} }}}$

$\dashrightarrow \quad \rm { Speed_{(Avg)} = \dfrac{1420}{27} \; km \: h^{-1}}$

$\dashrightarrow \quad\underline{\boxed{ \bf { Speed_{(Avg)} = 59.59 \; km \: h^{-1} }}}$

∴ The average speed of the man is 59.59 km/h.

Answer 2

Answer:

52.59 Km/h

Explanation:

Total distance = 800+420+200=1420 Km

Time taken in first section = 800/80=10hrs

Time taken in second section = 420/60=7hrs

Time taken in third section = 200/20=10hrs

Total Time taken = 10+7+10=27hrs

Average speed = Total distance/Total time taken

=1420/27=52.59 Km/h.