goldenlink7ydw

2023-02-21

A train travels from a city A to city B with a constant speed of 10 m/s and returns back to city A in half of the time taken to travel from A to B. Find its average speed during the entire journey.

A) 40 m/s

B) 30 m/s

C) 15 m/s

D) $\frac{40}{3}$ m/s

A) 40 m/s

B) 30 m/s

C) 15 m/s

D) $\frac{40}{3}$ m/s

reescameriama10

Beginner2023-02-22Added 4 answers

The correct answer is D) $\frac{40}{3}$ m/s

Let distance between the two cities A and B be x m.

Speed of train while going from A to B=10 m/s

Time taken by train to travel from A to B

${t}_{1}=\frac{x}{10}$

and time taken by train to travel from B to A

${t}_{2}=\frac{{t}_{1}}{2}=\frac{x}{20}$

Average speed $=\frac{\text{total distance}}{\text{total time}}$

${v}_{avg}=\frac{x+x}{\frac{x}{10}+\frac{x}{20}}$

Hence, ${v}_{avg}=\frac{2x}{\frac{x}{10}+\frac{x}{20}}=\frac{40}{3}m/s$

Let distance between the two cities A and B be x m.

Speed of train while going from A to B=10 m/s

Time taken by train to travel from A to B

${t}_{1}=\frac{x}{10}$

and time taken by train to travel from B to A

${t}_{2}=\frac{{t}_{1}}{2}=\frac{x}{20}$

Average speed $=\frac{\text{total distance}}{\text{total time}}$

${v}_{avg}=\frac{x+x}{\frac{x}{10}+\frac{x}{20}}$

Hence, ${v}_{avg}=\frac{2x}{\frac{x}{10}+\frac{x}{20}}=\frac{40}{3}m/s$