Speed, Time & Distance — Exercise 11(A)

A bus travels a distance of 186 km in 2 hours 35 minutes. What is the speed of the bus in km/hr?

Answer

Given,

Distance covered = 186 km

Time taken = 2 hours 35 minutes

= $2\dfrac{35}{60} \text{ hrs } = 2\dfrac{7}{12} \text{ hrs } = \dfrac{31}{12}$ hrs

By formula,

$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{186 \text{ km}}{\dfrac{31}{12} \text{ hrs}}\\[1em] = 186 \times \dfrac{12}{31} \text{ km/hr }\\[1em] = 72 \text{ km/hr }$

Hence, the speed of the bus is 72 km/hr.

A train covers 35 km in 25 minutes. What is the speed of the train in km/hr?

Answer

Given,

Distance covered = 35 km

Time taken = 25 minutes

= $\dfrac{25}{60} \text{ hr } = \dfrac{5}{12}$ hr

By formula,

$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{35 \text{ km}}{\dfrac{5}{12} \text{ hr}}\\[1em] = 35 \times \dfrac{12}{5} \text{ km/hr }\\[1em] = 84 \text{ km/hr }$

Hence, the speed of the train is 84 km/hr.

A man walks 8 km in 1 hour 20 minutes. What is the speed of the man in km/hr?

Answer

Given,

Distance covered = 8 km

Time taken = 1 hour 20 minutes

= $1\dfrac{20}{60} \text{ hrs } = 1\dfrac{1}{3} \text{ hrs } = \dfrac{4}{3}$ hrs

By formula,

$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{8 \text{ km}}{\dfrac{4}{3} \text{ hrs}}\\[1em] = 8 \times \dfrac{3}{4} \text{ km/hr }\\[1em] = 6 \text{ km/hr }$

Hence, the speed of the man is 6 km/hr.

A man cycles at 12 km per hour. How much distance does he cover in 35 minutes?

Answer

Given,

Speed = 12 km/hr

Time taken = 35 minutes

= $\dfrac{35}{60} \text{ hr } = \dfrac{7}{12}$ hr

By formula,

$\text{Distance} = \text{Speed} \times \text{Time}\\[1em] = 12 \times \dfrac{7}{12} \text{ km }\\[1em] = 7 \text{ km }$

Hence, the man covers 7 km in 35 minutes.

A car is travelling at a speed of 72 km/hr. How far will it travel in 25 minutes?

Answer

Given,

Speed = 72 km/hr

Time taken = 25 minutes

= $\dfrac{25}{60} \text{ hr } = \dfrac{5}{12}$ hr

By formula,

$\text{Distance} = \text{Speed} \times \text{Time}\\[1em] = 72 \times \dfrac{5}{12} \text{ km }\\[1em] = 30 \text{ km }$

Hence, the car will travel 30 km in 25 minutes.

A cyclist covers 1.5 km in 5 minutes. Find his speed in km/hr.

Answer

Given,

Distance covered = 1.5 km

Time taken = 5 minutes

= $\dfrac{5}{60} \text{ hr } = \dfrac{1}{12}$ hr

By formula,

$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{1.5 \text{ km}}{\dfrac{1}{12} \text{ hr}}\\[1em] = 1.5 \times 12 \text{ km/hr }\\[1em] = 18 \text{ km/hr }$

Hence, the speed of the cyclist is 18 km/hr.

Sajjal is going on his scooty at a speed of 24 km/hr. How much time will he take to cover 1 km 600 m?

Answer

Given,

Speed = 24 km/hr

Distance = 1 km 600 m

= $1\dfrac{600}{1000} \text{ km } = 1.6$ km

By formula,

$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{1.6 \text{ km}}{24 \text{ km/hr}}\\[1em] = \dfrac{1.6}{24} \text{ hr }\\[1em] = \dfrac{1}{15} \text{ hr }\\[1em] = \dfrac{1}{15} \times 60 \text{ min }\\[1em] = 4 \text{ min }$

Hence, Sajjal will take 4 minutes to cover 1 km 600 m.

Convert the following speed into m/sec:

36 km/hr

Answer

To convert a speed of km/hr into m/sec, we multiply by $\dfrac{5}{18}$.

$\Rightarrow 36 \text{ km/hr }= \left(36 \times \dfrac{5}{18}\right) \text{ m/sec }\\[1em] = \dfrac{180}{18} \text{ m/sec }\\[1em] = 10 \text{ m/sec }$

Hence, 36 km/hr = 10 m/sec.

Convert the following speed into m/sec:

81 km/hr

Answer

To convert a speed of km/hr into m/sec, we multiply by $\dfrac{5}{18}$.

$\Rightarrow 81 \text{ km/hr }= \left(81 \times \dfrac{5}{18}\right) \text{ m/sec }\\[1em] = \dfrac{405}{18} \text{ m/sec }\\[1em] = \dfrac{45}{2} \text{ m/sec }\\[1em] = 22\dfrac{1}{2} \text{ m/sec }$

Hence, 81 km/hr = $\mathbf{22\dfrac{1}{2}}$ m/sec.

Convert the following speed into m/sec:

9 km/hr

Answer

To convert a speed of km/hr into m/sec, we multiply by $\dfrac{5}{18}$.

$\Rightarrow 9 \text{ km/hr }= \left(9 \times \dfrac{5}{18}\right) \text{ m/sec }\\[1em] = \dfrac{45}{18} \text{ m/sec }\\[1em] = \dfrac{5}{2} \text{ m/sec }\\[1em] = 2\dfrac{1}{2} \text{ m/sec }$

Hence, 9 km/hr = $\mathbf{2\dfrac{1}{2}}$ m/sec.

Convert the following speed into km/hr:

25 m/sec

Answer

To convert a speed of m/sec into km/hr, we multiply by $\dfrac{18}{5}$.

$\Rightarrow 25 \text{ m/sec }= \left(25 \times \dfrac{18}{5}\right) \text{ km/hr }\\[1em] = \dfrac{450}{5} \text{ km/hr }\\[1em] = 90 \text{ km/hr }$

Hence, 25 m/sec = 90 km/hr.

Convert the following speed into km/hr:

7.5 m/sec

Answer

To convert a speed of m/sec into km/hr, we multiply by $\dfrac{18}{5}$.

$\Rightarrow 7.5 \text{ m/sec }= \left(7.5 \times \dfrac{18}{5}\right) \text{ km/hr }\\[1em] = \dfrac{135}{5} \text{ km/hr }\\[1em] = 27 \text{ km/hr }$

Hence, 7.5 m/sec = 27 km/hr.

Convert the following speed into km/hr:

1 m/sec

Answer

To convert a speed of m/sec into km/hr, we multiply by $\dfrac{18}{5}$.

$\Rightarrow 1 \text{ m/sec }= \left(1 \times \dfrac{18}{5}\right) \text{ km/hr }\\[1em] = \dfrac{18}{5} \text{ km/hr }\\[1em] = 3\dfrac{3}{5} \text{ km/hr }$

Hence, 1 m/sec = $\mathbf{3\dfrac{3}{5}}$ km/hr.

A train covers 120 m in 5 seconds. What is the speed of the train in km/hr?

Answer

Given,

Distance covered = 120 m

Time taken = 5 seconds

By formula,

$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{120 \text{ m}}{5 \text{ sec}}\\[1em] = 24 \text{ m/sec }$

Converting the speed into km/hr :

$\Rightarrow 24 \text{ m/sec } = \left(24 \times \dfrac{18}{5}\right) \text{ km/hr }\\[1em] = \dfrac{432}{5} \text{ km/hr }\\[1em] = 86\dfrac{2}{5} \text{ km/hr }$

Hence, the speed of the train is $\mathbf{86\dfrac{2}{5}}$ km/hr.

A bus is moving at a speed of 84 km/hr. How much distance will it cover in 1 min 45 sec.?

Answer

Given,

Speed = 84 km/hr

Time taken = 1 min 45 sec = (60 + 45) sec = 105 sec

Converting the speed into m/sec :

$84 \text{ km/hr } = \left(84 \times \dfrac{5}{18}\right) \text{ m/sec }\\[1em] = \dfrac{70}{3} \text{ m/sec }$

By formula,

$\text{Distance} = \text{Speed} \times \text{Time}\\[1em] = \dfrac{70}{3} \times 105 \text{ m }\\[1em] = 70 \times 35 \text{ m }\\[1em] = 2450 \text{ m }\\[1em] = 2 \text{ km } 450 \text{ m }$

Hence, the bus will cover 2 km 450 m.

Preeti is going on her moped at a speed of 24 km/hr. How much time will she take to cover 720 metres?

Answer

Given,

Speed = 24 km/hr

Distance = 720 m

Converting the speed into m/sec :

$24 \text{ km/hr } = \left(24 \times \dfrac{5}{18}\right) \text{ m/sec }\\[1em] = \dfrac{20}{3} \text{ m/sec }$

By formula,

$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{720 \text{ m}}{\dfrac{20}{3} \text{ m/sec}}\\[1em] = 720 \times \dfrac{3}{20} \text{ sec }\\[1em] = 108 \text{ sec }\\[1em] = 1 \text{ min } 48 \text{ sec }$

Hence, Preeti will take 108 sec = 1 min 48 sec to cover 720 metres.

A car, running at 45 km/hr, takes 6 hours to complete a journey. At what speed must it travel to complete the journey in 5 hours?

Answer

Given,

Speed = 45 km/hr

Time taken = 6 hours

By formula,

$\text{Distance} = \text{Speed} \times \text{Time}\\[1em] = 45 \times 6 \text{ km }\\[1em] = 270 \text{ km }$

New time taken = 5 hours

$\text{New speed} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{270 \text{ km}}{5 \text{ hrs}}\\[1em] = 54 \text{ km/hr }$

Hence, the car must travel at a speed of 54 km/hr to complete the journey in 5 hours.

A car covers a certain distance in 40 minutes, if it runs at 54 km/hr. How much time will it take to cover the same distance at a speed 45 km/hr?

Answer

Given,

Speed = 54 km/hr

Time taken = 40 minutes

= $\dfrac{40}{60} \text{ hr } = \dfrac{2}{3}$ hr

By formula,

$\text{Distance} = \text{Speed} \times \text{Time}\\[1em] = 54 \times \dfrac{2}{3} \text{ km }\\[1em] = 36 \text{ km }$

New speed = 45 km/hr

$\text{New time} = \dfrac{\text{Distance}}{\text{Speed}} = \dfrac{36 \text{ km}}{45 \text{ km/hr}}\\[1em] = \dfrac{4}{5} \text{ hr }\\[1em] = \dfrac{4}{5} \times 60 \text{ min }\\[1em] = 48 \text{ min }$

Hence, the car will take 48 minutes to cover the same distance at a speed of 45 km/hr.