Speed, Time & Distance — Competency Focused Questions

A plane flies from City A to City B, covering a distance of 1,200 km in 2 hours. The return trip takes 2 hours and 48 minutes due to strong headwinds. What is the average speed of the plane for the entire journey?

$\left[\text{Average speed} = \dfrac{\text{total distance covered}}{\text{total time taken}}\right]$

1. 500 km/h

2. 540 km/h

3. 480 km/h

4. 490 km/h

Answer

Given,

Total distance covered = 1200 km + 1200 km = 2400 km

Total time taken = 2 hrs + 2 hrs 48 min

= $2 \text{ hrs} + 2\dfrac{48}{60} \text{ hrs } = 2 \text{ hrs} + 2\dfrac{4}{5} \text{ hrs } = 2 \text{ hrs} + 2.8 \text{ hrs } = 4.8$ hrs

By formula,

$\text{Average speed} = \dfrac{\text{Total distance covered}}{\text{Total time taken}}\\[1em] = \dfrac{2400 \text{ km}}{4.8 \text{ hrs}}\\[1em] = 500 \text{ km/h }$

Hence, option 1 is the correct option.

Two runners, Ramesh and Suresh, start at the same point but run on two different circular tracks.

• Ramesh completes one round of a 300 m track in 1 minute.

• Suresh completes one round of a 400 m track in 1.5 minutes.

Who will be ahead after 6 minutes, and by how much distance?

1. Ramesh, by 200 m

2. Suresh, by 300 m

3. Ramesh, by 900 m

4. Both will be at the same point

Answer

Given,

Ramesh covers 300 m in 1 minute and Suresh covers 400 m in 1.5 minutes.

By formula,

$\text{Speed of Ramesh} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{300 \text{ m}}{1 \text{ min}}\\[1em] = 300 \text{ m/min }$

Distance covered by Ramesh in 6 minutes = 300 × 6 m = 1800 m

$\text{Speed of Suresh} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{400 \text{ m}}{1.5 \text{ min}}\\[1em] = \dfrac{800}{3} \text{ m/min }$

Distance covered by Suresh in 6 minutes = $\dfrac{800}{3} \times 6$ m = 1600 m

Since, 1600 m < 1800 m, Ramesh will be ahead.

Difference of distances = 1800 m − 1600 m = 200 m

Hence, option 1 is the correct option.

Two friends, Amit and Sunil, start at the same point and walk in opposite directions. Amit walks at 4 km/h, and Sunil walks at 5 km/h. After 3 hours, how far apart will they be?

1. 9 km

2. 15 km

3. 18 km

4. 27 km

Answer

Given,

Speed of Amit = 4 km/h, speed of Sunil = 5 km/h and time taken = 3 hours

As Amit and Sunil walk in opposite directions,

Relative speed = 4 km/h + 5 km/h = 9 km/h

By formula,

$\text{Distance between them} = \text{Relative speed} \times \text{Time}\\[1em] = 9 \times 3 \text{ km }\\[1em] = 27 \text{ km }$

Hence, option 4 is the correct option.

A person leaves their house at 8:00 am, walks 6 km at 4 km/h, and then cycles another 12 km at 12 km/h to reach their workplace. What time does the person reach their workplace?

1. 10:30 am

2. 9:15 am

3. 9:20 am

4. 9:10 am

Answer

Given,

Distance walked = 6 km at a speed of 4 km/h and distance cycled = 12 km at a speed of 12 km/h

By formula,

$\text{Time taken in walking} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{6 \text{ km}}{4 \text{ km/h}}\\[1em] = \dfrac{3}{2} \text{ hrs }\\[1em] = 1 \text{ hr } 30 \text{ min }$

$\text{Time taken in cycling} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{12 \text{ km}}{12 \text{ km/h}}\\[1em] = 1 \text{ hr }$

Total time taken = 1 hr 30 min + 1 hr = 2 hrs 30 min

Time of reaching the workplace = 8:00 am + 2 hrs 30 min = 10:30 am

Hence, option 1 is the correct option.

A car completes a certain journey in 8 hours. It covers half the distance at 40 km/h and the rest at 60 km/h. The length of the journey is:

1. 300 km

2. 350 km

3. 364 km

4. 384 km

Answer

Let the length of the journey be 2x km, so that each half of the journey is x km.

By formula,

Time taken to cover the first half = $\dfrac{\text{Distance}}{\text{Speed}} = \dfrac{x}{40}$ hrs

Time taken to cover the second half = $\dfrac{\text{Distance}}{\text{Speed}} = \dfrac{x}{60}$ hrs

Total time taken = 8 hrs

$\Rightarrow \dfrac{x}{40} + \dfrac{x}{60} = 8\\[1em] \Rightarrow \dfrac{3x + 2x}{120} = 8\\[1em] \Rightarrow \dfrac{5x}{120} = 8\\[1em] \Rightarrow x = \dfrac{8 \times 120}{5}\\[1em] \Rightarrow x = 192$

Length of the journey = 2x km = 2 × 192 km = 384 km

Hence, option 4 is the correct option.