Class 8: Time and Distance – Exercise 12A – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Question 1: Express the following speeds in meter/sec:

i) $72$ km/hr ii) $117$ km/hr iii) $5.4$ km/hr iv) $12.6$ km/hr

Answer:

i) $72\hspace{2pt}$ $\frac{km}{hr} = \frac{72\times 1000 \ m}{3600 \ sec}$ $= 20\hspace{2pt}$ $\frac{m}{s}$

ii) $117\hspace{2pt}$ $\frac{km}{hr} = \frac{117\times 1000 \ m}{3600 \ sec}$ $= 32.5\hspace{2pt}$ $\frac{ m}{s}$

iii) $5.4\hspace{2pt}$ $\frac{km}{hr} = \frac{5.4\times 1000 \ m}{3600 \ sec}$ $= 1.5\hspace{2pt}$ $\frac{ m}{s}$

iv) $12.6\hspace{2pt}$ $\frac{km}{hr} = \frac{12.6 \times 1000 \ m}{3600 \ sec}$ $= 3.5\hspace{2pt}$ $\frac{m}{s}$

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Question 2: Express the following speeds in km/hr:

i) $18$ m/sec ii) $2$ m/sec iii) $3$ $\frac{1}{3}$ m/sec iv) $12.5$ m/sec

Answer:

i) $18\hspace{2pt}$ $\frac{m}{s} = \frac{18 \ km \times 3600}{1000 \ hr}$ $= 64.8\hspace{2pt}$ $\frac{km}{hr}$

ii) $2\hspace{2pt}$ $\frac{m}{s} = \frac{2 \ km \times 3600}{1000 \ hr}$ $= 7.2\hspace{2pt}$ $\frac{km}{hr}$

iii) $3\frac{1}{3}\hspace{2pt}$ $\frac{m}{s} = \frac{10 \ km \times 3600}{3 \times 1000 \ hr}$ $= 12\hspace{2pt}$ $\frac{km}{hr}$

iv) $12.5\hspace{2pt}$ $\frac{m}{s} = \frac{12.5 \ km \times 3600}{1000 \ hr}$ $= 45\hspace{2pt}$ $\frac{km}{hr}$

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Question 3: An athlete covers a distance of $1200$ meters in $4$ minutes $48$ seconds. Find his speed in km/hr.

Answer:

$Speed =$ $\frac{1200 \ m}{4 min \ 48 \ sec} = \frac{1200 \ km \times 3600}{1000 \times 288 \ hr}$ $= 15\hspace{2pt}\frac{km}{hr}$

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Question 4: Walking at the rate of $4$ km/hr a man covers a certain distance in $2\frac{1}{2}$ hours. How much time will be taken by the man to cover the same distance, if he cycles at $12$ km/hr?

Answer:

Distance covered walking $= 4 \times 2.5 = 10 km$

Time to cover 10 km on cycle $=$ $\frac{10 \ km \times hr}{12 \ km} = \frac{5}{6}$ $hr$ or 50 minutes

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Question 5: A car can finish a certain journey in $10$ hours at a speed of $48$ km/hr. By how much the speed of car must be increased to cover the same distance in $8$ hours?

Answer:

Distance covered by the car $= 48 \times 10 = 480 km$

Speed to cover the same distance in 8 hr $=$ $\frac{480 \ km}{8 \ hr}$ $= 60$ $\frac{km}{hr}$

Hence the speed must be increased by $= 60 -48 = 12\hspace{2pt} \frac{km}{hr}$

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Question 6: A bus covers a certain distance in $50$ minutes, if it runs at a speed of $54$ km/hr. What must be the speed of the bus in order to reduce the time of journey to $40$ minutes?

Answer:

Distance covered by the bus $=$ $\frac{50}{60}$ $\times 54 = 45 \frac{km}{hr}$

Speed to cover the same distance in 40 min $=$ $\frac{45 \ km \times 60}{40 \ hr }$ $= 67.5 \frac{km}{hr}$

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Question 7: A motor car starts with the speed of $70$ km/hr with its speed increasing every two hours by $10$ km/hr. In how much time will it cover a distance of $345$ km?

Answer:

Speed at the start $= 70\frac{km}{hr}$

Distance covered in first 2 hours $= 140 \frac{km}{hr}$

Speed After 2 hours $= 80 \frac{km}{hr}$

Distance covered in 3rd and the 4th hour $= 160 km$

Total distance covered by end of 4th hours $= 140 + 160 = 300 km$

Distance left to be covered after end of 4th hour $= 345 - 300 = 45 km$

Speed After 4 hours $= 90 \frac{km}{hr}$

Time taken to cover 45 km at speed of $90 \frac{km}{hr} = 0.5 hr$

Hence the total time to cover $345 km = 4.5 hr$

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Question 8: A man takes $150$ steps in walking $75$ meters. If he takes $3$ steps in $1$ second, find his speed in (i) m/sec (ii) km/hr.

Answer:

Length of one step $=$ $\frac{75}{150}$ $= 0.5 m$

Distance covered in 1 sec $= 0.5\times3 = 1.5 \frac{m}{s}$

i) Speed in $\frac{m}{s} = 1.5 \frac{m}{s}$
ii) Speed in $\frac{km}{hr} =$ $\frac{1.5 km \times 3600}{1000\times hr}$ $= 5.4 \frac{km}{hr}$

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Question 9: A man walks at $5$ km/hr for $6$ hours and at $4$ km/hr for $12$ hours. Find his average speed.

Answer:

Average Speed $=$ $\frac{Distance \ Covered}{Total \ time \ taken \ to \ cover \ the distance}$

Average Speed $=$ $\frac{5 \times 6 + 4 \times 12}{6 + 12}$ $= 4$ $\frac{1}{3} \frac{km}{hr}$

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Question 10: A man covers a distance of $144$ km at the speed of $36$ km/hr and another $256$ km at the speed of $64$ km/hr. Find his average speed for the whole journey.

Answer:

Average Speed $=$ $\frac{Distance \ Covered}{Total \ time \ taken \ to \ cover \ the distance}$

Average Speed $=$ $\frac{144 +256}{\frac{144}{36} + \frac{256}{64}}$ $= 50 \frac{km}{hr}$

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Question 11: Two buses travel to a place at $45$ km/hr and $60$ km/hr respectively. If the second bus takes $5\frac{1}{2} hr$ hours less than the first for the same journey, find the length of the journey.

Answer:

Let $x$ be the distance of the journey

Time taken by the First bus $=$ $\frac{x}{45}$ $hr$

Time taken by the Second bus $=$ $\frac{x}{60}$ $hr$

Therefore $\colon$ $\frac{x}{45}- \frac{x}{60} = \frac{11}{2}$

Solving for $x = 990 km$

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Question 12: A boy goes to school from his village at $3$ km/hr and returns back at $2$ km/hr. If he takes $5$ hours in all, what is the distance between the village and the school?

Answer:

Let $x$ be the distance of the journey

Time taken to reach school $=$ $\frac{x}{3}$ $hr$

Time taken return from $=$ $\frac{x}{2}$ $hr$

Therefore $\colon$ $\frac{x}{3} + \frac{x}{2}$ $= 5$

Solving for $x = 6 km$

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Question 13: A bus completes a journey of $420$ km in $6\frac{1}{2} hr$ . The first $\frac{3}{4}$ part of the journey performed at $63$ km/hr. Calculate the speed of the rest of the journey.

Answer:

Let $x$ be the speed of the rest of the journey

$\Rightarrow$ $\frac{3}{4}$ $\times 420 \times$ $\frac{1}{63}$ $+$ $\frac{105}{x}$ $= 6$ $\frac{1}{2}$

Solving for $x = 70 \frac{km}{hr}$

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Question 14: A man drives $150$ km from town A to town B in $3$ hours $20$ min and returns back to town A from town B in $4$ hours $10$ min. Find his average speed for the whole journey.

Answer:

Average Speed $=$ $\frac{Distance \ Covered}{Total \ time \ taken \ to \ cover \ the distance}$

Average Speed $=$ $\frac{150 + 150}{3\frac{1}{3} + 4\frac{1}{6}}$ $= 40 \frac{km}{hr}$

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Question 15: A car completed a journey in $7$ hours. One-third of the journey was performed at $20$ km/hr and the rest at $30$ km/hr. Find the total length of the journey.

Answer:

Let $x$ be the distance of the journey.

$\frac{\frac{x}{3}}{20} + \frac{\frac{2x}{3}}{30}$ $= 7$

Solving for $x = 180 \ km$

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Question 16: A cyclist covered a certain distance in $3$ $\frac{1}{2}$ hours. The speed for first half of the distance was $15$ km/hr and for the second half it was $20$ km/hr. Find the total distance covered by him.

Answer:

Let $x$ be the distance of the journey.

$\frac{\frac{x}{2}}{15} + \frac{\frac{x}{2}}{20}$ $= 3$ $\frac{1}{2}$

Solving for $x = 60 \ km$

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Question 17: A person travels equal distances with speeds of $3$ km/hr, $4$ km/hr and $5$ km/hr and takes a total time of $47$ minutes. Find the total distance.

Answer:

Let $x$ be the distance of each leg

$\frac{x}{3} + \frac{x}{4} + \frac{x}{5} = \frac{47}{60}$

Solving for $x = 1 \ km$ and the total distance is $3 \ km$

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Question 18: A farmer traveled a distance of $61$ km in $9$ hours. He traveled partly on foot at $4$ km/hr and partly on bicycle at $9$ km/hr. Find the distance traveled by him on foot.

Answer:

Let $x$ be the distance traveled by foot

$\frac{x}{4} + \frac{61 - x}{9}$ $= 9$

Solving for $x = 16 \ km$

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Question 19: Rohan cycles to his office at the rate of $12$ $\frac{1}{2}$ km/hr and is late by $3$ minutes. However, if he travels at $15$ km/hr, he reaches $5$ minutes earlier than the usual time. What is the distance of his office from his residence?

Answer:

Let $x$ be the distance to office. The difference of the time in the two cases is 8 minutes.

$\frac{x}{12.5} - \frac{x}{15} = \frac{8}{60}$

Solving for $x=10 \ km$ (Distance of his office from his residency)

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Question 20: Robert is travelling on his cycle and has calculated to reach point A at 2 p.m. if he travels at $10$ km/hr. However, he will reach there at 12 noon if he travels at $15$ km/hr. At what speed must he travel to reach A at 1 p.m.?

Answer:

Let the distance traveled $= x km$

$\frac{x}{10} - \frac{x}{15}$ $=2$

Solving for $x=60 \ km$

$\frac{60}{10} - \frac{60}{s}$ $=1$

Solving for $s=12 \frac{km}{hr}$

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Question 21: If a train runs at $40$ km/hr, it reaches its destination late by $11$ minutes, but if it runs at $50$ km/hr, it is late by $5$ minutes only. Find the correct time for the train to complete its journey.

Answer:

Let the distance traveled by the train $= x \ km$

$\frac{x}{40} - \frac{x}{50} = \frac{6}{60}$

Solving for $x = 20 \ km$ (Distance of his office from his residency)

Time taken to cover 20 km=30 minutes

Therefore the correct time is 19 minutes

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Question 22: The distance between Delhi and Hyderabad is $1800$ km. A train leaves Delhi and proceeds towards Hyderabad at a uniform speed of $60$ km/hr. Another train leaves Hyderabad at the same time and proceeds towards Delhi at a uniform speed of $48$ km/hr. When and where will they meet?