Q: In a circular race of $750\text{ m}$, X and Y start at speeds of $9\text{ km/h}$ and $13.5\text{ km/h}$. If they run in the same direction, when will they meet again for the first time?

$600\text{ s}$ — Relative speed = $13.5 - 9 = 4.5\text{ km/h} = 4.5 \times \frac{5}{18} = 1.25\text{ m/s}$. Time = $\frac{\text{Distance}}{\text{Relative Speed}} = \frac{750}{1.25} = 600\text{ seconds}$.

Q: A bus travels $\frac{1}{3}$ of the distance at $40\text{ km/h}$, the next $\frac{1}{3}$ at $50\text{ km/h}$, and the final $\frac{1}{3}$ at $60\text{ km/h}$. Find the average speed.

$48.65\text{ km/h}$ — Average speed = $\frac{3}{\frac{1}{40} + \frac{1}{50} + \frac{1}{60}} = \frac{3 \times 600}{15 + 12 + 10} = \frac{1800}{37} \approx 48.65\text{ km/h}$.

Q: A taxi travels at a constant speed of 75 km/h to cover a certain distance in 3 hours and 12 minutes. If road construction increases the time taken by 24 minutes, by what percentage must the taxi's average speed decrease to complete the journey?

11.11% — Time = 3 hrs 12 mins = 3.2 hrs. Distance = $75 \times 3.2 = 240$ km. New time = 3.2 hrs + 24 mins (0.4 hrs) = 3.6 hrs. New speed = $240 / 3.6 = 66.66$ km/h. Decrease = $75 - 66.66 = 8.33$. % Decrease = $\frac{8.33}{75} \times 100 = 11.11\%$.

Q: A person cycles from home to work at a speed of 8 km/h and reaches 18 minutes late. If he increases his speed to 12 km/h, he reaches 6 minutes early. What is the distance (in km) from home to work?

9.6 km — Time difference = $18 \text{ (late)} + 6 \text{ (early)} = 24 \text{ minutes} = \frac{24}{60} \text{ hours} = 0.4 \text{ hours}$. Equation: $\frac{D}{8} - \frac{D}{12} = 0.4 \implies \frac{3D - 2D}{24} = 0.4 \implies D = 24 \times 0.4 = 9.6$ km.

Question 1

In a circular race of $750	ext{ m}$, X and Y start at speeds of $9	ext{ km/h}$ and $13.5	ext{ km/h}$. If they run in the same direction, when will they meet again for the first time?

Accepted Answer

$600	ext{ s}$ — Relative speed = $13.5 - 9 = 4.5	ext{ km/h} = 4.5 	imes \frac{5}{18} = 1.25	ext{ m/s}$. Time = $\frac{	ext{Distance}}{	ext{Relative Speed}} = \frac{750}{1.25} = 600	ext{ seconds}$.

Question 2

A bus travels $\frac{1}{3}$ of the distance at $40	ext{ km/h}$, the next $\frac{1}{3}$ at $50	ext{ km/h}$, and the final $\frac{1}{3}$ at $60	ext{ km/h}$. Find the average speed.

Accepted Answer

$48.65	ext{ km/h}$ — Average speed = $\frac{3}{\frac{1}{40} + \frac{1}{50} + \frac{1}{60}} = \frac{3 	imes 600}{15 + 12 + 10} = \frac{1800}{37} \approx 48.65	ext{ km/h}$.

Question 3

A taxi travels at a constant speed of 75 km/h to cover a certain distance in 3 hours and 12 minutes. If road construction increases the time taken by 24 minutes, by what percentage must the taxi's average speed decrease to complete the journey?

Accepted Answer

11.11% — Time = 3 hrs 12 mins = 3.2 hrs. Distance = $75 	imes 3.2 = 240$ km. New time = 3.2 hrs + 24 mins (0.4 hrs) = 3.6 hrs. New speed = $240 / 3.6 = 66.66$ km/h. Decrease = $75 - 66.66 = 8.33$. % Decrease = $\frac{8.33}{75} 	imes 100 = 11.11\%$.

Question 4

A person cycles from home to work at a speed of 8 km/h and reaches 18 minutes late. If he increases his speed to 12 km/h, he reaches 6 minutes early. What is the distance (in km) from home to work?

Accepted Answer

9.6 km — Time difference = $18 	ext{ (late)} + 6 	ext{ (early)} = 24 	ext{ minutes} = \frac{24}{60} 	ext{ hours} = 0.4 	ext{ hours}$. Equation: $\frac{D}{8} - \frac{D}{12} = 0.4 \implies \frac{3D - 2D}{24} = 0.4 \implies D = 24 	imes 0.4 = 9.6$ km.

Question 5

An airplane travels a specific distance at a speed of 240 km/h over the course of 5 hours. To cover the same distance in just 1 hour, it needs to fly at a speed of:

Accepted Answer

1200 km/h — Distance = Speed * Time = 240 * 5 = 1200 km. Required Speed for 1 hour = 1200 / 1 = 1200 km/h.

Question 6

A person travels from city A to city B. If he travels at a speed of 50 km/h, he arrives 1 hour early. If he travels at a speed of 30 km/h, he arrives 1 hour late. What is the distance (in km) between city A and city B?

Accepted Answer

150 km — Let the actual time be t hours. Distance = 50 * (t - 1) = 30 * (t + 1) -> 50t - 50 = 30t + 30 -> 20t = 80 -> t = 4 hours. Distance = 50 * (4 - 1) = 150 km.

Question 7

In a circular race of 840 m, A and B start running in the same direction at the same time from the same point at the speeds of 6 m/s and 12 m/s, respectively. After how much time will they meet next?

Accepted Answer

140 s — Time to meet = Track Length / Relative Speed = 840 / (12 - 6) = 840 / 6 = 140 seconds.

Question 8

Varun and Sandeep started for a car race from the same point, in the same direction and at the same time on a circular track of length 1635 m with the speeds of 90 km/h and 108 km/h, respectively. After how much time (in s) will they meet again for the first time?

Accepted Answer

327 — Speeds in m/s: 90 km/h = 25 m/s, 108 km/h = 30 m/s. Relative speed (same direction) = 30 - 25 = 5 m/s. Time taken to meet = Track Length / Relative Speed = 1635 / 5 = 327 seconds.

Time, Speed & Distance — Questions with Solutions

Q1. In a circular race of $750\text{ m}$, X and Y start at speeds of $9\text{ km/h}$ and $13.5\text{ km/h}$. If they run in the same direction, when will they meet again for the first time?

Q2. A bus travels $\frac{1}{3}$ of the distance at $40\text{ km/h}$, the next $\frac{1}{3}$ at $50\text{ km/h}$, and the final $\frac{1}{3}$ at $60\text{ km/h}$. Find the average speed.

Q3. A taxi travels at a constant speed of 75 km/h to cover a certain distance in 3 hours and 12 minutes. If road construction increases the time taken by 24 minutes, by what percentage must the taxi's average speed decrease to complete the journey?

Q4. A person cycles from home to work at a speed of 8 km/h and reaches 18 minutes late. If he increases his speed to 12 km/h, he reaches 6 minutes early. What is the distance (in km) from home to work?

Q5. An airplane travels a specific distance at a speed of 240 km/h over the course of 5 hours. To cover the same distance in just 1 hour, it needs to fly at a speed of:

Q6. A person travels from city A to city B. If he travels at a speed of 50 km/h, he arrives 1 hour early. If he travels at a speed of 30 km/h, he arrives 1 hour late. What is the distance (in km) between city A and city B?

Q7. In a circular race of 840 m, A and B start running in the same direction at the same time from the same point at the speeds of 6 m/s and 12 m/s, respectively. After how much time will they meet next?

Q8. Varun and Sandeep started for a car race from the same point, in the same direction and at the same time on a circular track of length 1635 m with the speeds of 90 km/h and 108 km/h, respectively. After how much time (in s) will they meet again for the first time?