Idea of Speed, Distance & Time — Exercise 11(A)

A train covers 51 km in 3 hours. Calculate its speed. How far does the train go in 30 minutes?

Answer

Given,

Distance covered = 51 km and time taken = 3 hours.

Speed = $\dfrac{\text{Distance}}{\text{Time}} = \dfrac{51}{3} = 17$ km/h.

Converting 30 minutes into hours :

30 minutes = $\dfrac{30}{60}$ h = $\dfrac{1}{2}$ h.

Distance covered in 30 minutes = Speed × Time = 17 × $\dfrac{1}{2}$ = 8.5 km.

Hence, the speed of the train = 17 km/h and it goes 8.5 km in 30 minutes.

A motorist travelled the distance between two towns, which is 65 km, in 2 hours and 10 minutes. Find his speed in metre per minute.

Answer

Given,

Distance = 65 km and time = 2 hours 10 minutes.

As the speed is required in metre per minute, convert the distance into metres and the time into minutes.

Distance = 65 km

= 65 × 1000 m

= 65000 m.

Time = 2 hours 10 minutes

= (2 × 60 + 10) minutes

= 130 minutes.

Speed = $\dfrac{\text{Distance}}{\text{Time}} = \dfrac{65000}{130} = 500$ m/min.

Hence, the speed of the motorist = 500 m/min.

A train travels 700 metres in 35 seconds. What is its speed in km h^-1?

Answer

Given,

Distance = 700 metres and time = 35 seconds.

Speed = $\dfrac{\text{Distance}}{\text{Time}} = \dfrac{700}{35} = 20$ m/s.

Converting the speed into km/h (multiply by $\dfrac{18}{5}$) :

Speed = 20 × $\dfrac{18}{5} = \dfrac{360}{5} = 72$ km/h.

Hence, the speed of the train = 72 km/h.

A racing car covered 600 km in 3 hours 20 minutes. Find its speed in metre per second. How much distance will the car cover in 50 sec?

Answer

Given,

Distance = 600 km and time = 3 hours 20 minutes.

As the speed is required in metre per second, convert the distance into metres and the time into seconds.

Distance = 600 km

= 600 × 1000 m

= 600000 m.

Time = 3 hours 20 minutes

= (3 × 3600 + 20 × 60) seconds

= (10800 + 1200) seconds

= 12000 seconds.

Speed = $\dfrac{\text{Distance}}{\text{Time}} = \dfrac{600000}{12000} = 50$ m/s.

Distance covered in 50 seconds = Speed × Time = 50 × 50 = 2500 m.

Hence, the speed of the car = 50 m/s and it covers 2500 m in 50 seconds.

Rohit goes 350 km in 5 hours. Find:

(i) his speed

(ii) the distance covered by Rohit in 6.2 hours

(iii) the time taken by him to cover 210 km.

[Assume that throughout the journey, the speed of Rohit remains uniform].

Answer

Given,

Distance = 350 km and time = 5 hours.

(i) Speed = $\dfrac{\text{Distance}}{\text{Time}} = \dfrac{350}{5} = 70$ km/h.

Hence, Rohit's speed = 70 km/h.

(ii) Distance covered in 6.2 hours = Speed × Time = 70 × 6.2 = 434 km.

Hence, the distance covered by Rohit in 6.2 hours = 434 km.

(iii) Time taken to cover 210 km = $\dfrac{\text{Distance}}{\text{Speed}} = \dfrac{210}{70} = 3$ hours.

Hence, the time taken to cover 210 km = 3 hours.

A boy drives his scooter with a uniform speed of 45 km h^-1. Find:

(i) the distance covered by him in 1 hour 20 min.

(ii) the time taken by him to cover 108 km.

(iii) the time taken to cover 900 m.

Answer

Given,

Uniform speed of the scooter = 45 km/h.

(i) Time = 1 hour 20 min

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

Distance covered = Speed × Time

= 45 × $\dfrac{4}{3} = \dfrac{180}{3}$

= 60 km.

Hence, the distance covered in 1 hour 20 min = 60 km.

(ii) Time taken to cover 108 km = $\dfrac{\text{Distance}}{\text{Speed}}$

= $\dfrac{108}{45}$

= $\dfrac{12}{5}$

= 2.4 hours.

0.4 hour = 0.4 × 60 minutes = 24 minutes.

Hence, the time taken to cover 108 km = 2.4 hours (i.e. 2 hours 24 minutes).

(iii) 900 m = $\dfrac{900}{1000}$ km = 0.9 km.

Time taken to cover 900 m = $\dfrac{\text{Distance}}{\text{Speed}} = \dfrac{0.9}{45} = 0.02$ h.

0.02 h = 0.02 × 3600 seconds = 72 seconds.

Hence, the time taken to cover 900 m = 72 seconds.

I travel a distance of 10 km and come back in $2\dfrac{1}{2}$ hours. What is my speed?

Answer

Given,

Distance travelled one way = 10 km, so total distance = 10 km + 10 km = 20 km.

Total time taken = $2\dfrac{1}{2}$ hours = $\dfrac{5}{2}$ hours.

$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}} \\[1em] = \dfrac{20}{\dfrac{5}{2}} \\[1em] = \dfrac{40}{5} \\[1em] = 8 \text{ km/h}.$

Hence, my speed = 8 km/h.

A man walks a distance of 5 km in 2 hours. Then he goes in a bus to a nearby town, which is 40 km, in further 2 hours. From there, he goes to his office in an autorickshaw, a distance of 5 km, in $\dfrac{1}{2}$ hour. What was his average speed during the whole journey?

Answer

Given,

Distance walked = 5 km in 2 hours.

Distance by bus = 40 km in 2 hours.

Distance by autorickshaw = 5 km in $\dfrac{1}{2}$ hour.

Total distance covered = 5 km + 40 km + 5 km = 50 km.

Total time taken = 2 h + 2 h + $\dfrac{1}{2}$ h = $\dfrac{9}{2}$ h.

$\text{Average speed} = \dfrac{\text{Total distance covered}}{\text{Total time taken}} \\[1em] = \dfrac{50}{\dfrac{9}{2}} \\[1em] = 50 \times \dfrac{2}{9} \\[1em] = \dfrac{100}{9} \\[1em] = 11\dfrac{1}{9} \text{ km/h}.$

Hence, the man's average speed during the whole journey = $11\dfrac{1}{9}$ km/h.

Jagan went to another town such that he covered 240 km by a car going at 60 km h^-1. Then he covered 80 km by a train going at 100 km h^-1, and the rest 200 km he covered by a bus going at 50 km h^-1. What was his average speed during the whole journey?

Answer

Given,

Distance by car = 240 km at 60 km/h.

Distance by train = 80 km at 100 km/h.

Distance by bus = 200 km at 50 km/h.

Time taken by car = $\dfrac{240}{60} = 4$ hours.

Time taken by train = $\dfrac{80}{100} = \dfrac{4}{5} = 0.8$ hour.

Time taken by bus = $\dfrac{200}{50} = 4$ hours.

Total distance covered = 240 km + 80 km + 200 km = 520 km.

Total time taken = 4 h + 0.8 h + 4 h = 8.8 h = $\dfrac{44}{5}$ h.

$\text{Average speed} = \dfrac{\text{Total distance covered}}{\text{Total time taken}} \\[1em] = \dfrac{520}{\dfrac{44}{5}} \\[1em] = 520 \times \dfrac{5}{44} \\[1em] = \dfrac{2600}{44} \\[1em] = \dfrac{650}{11} \\[1em] = 59\dfrac{1}{11} \text{ km/h}.$

Hence, Jagan's average speed during the whole journey = $59\dfrac{1}{11}$ km/h.

The speed of sound in air is about 330 m s^-1. Express this speed in km h^-1. How long will the sound take to travel 99 km?

Answer

Given,

Speed of sound = 330 m/s.

Converting the speed into km/h (multiply by $\dfrac{18}{5}$) :

Speed = 330 × $\dfrac{18}{5} = \dfrac{5940}{5} = 1188$ km/h.

Time taken to travel 99 km = $\dfrac{\text{Distance}}{\text{Speed}} = \dfrac{99}{1188} = \dfrac{1}{12}$ h.

$\dfrac{1}{12}$ h = $\dfrac{1}{12}$ × 60 minutes = 5 minutes.

Hence, the speed of sound = 1188 km/h and it takes 5 minutes to travel 99 km.