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

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

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

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

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

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

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

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

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

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

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

Answer:

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

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

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  $= 60 -48 = 12\hspace{2pt} \frac{km}{hr}$

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   $=$ $\frac{45 \ km \times 60}{40 \ hr }$ $= 67.5 \frac{km}{hr}$

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  $345 km = 4.5 hr$

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 $= 0.5\times3 = 1.5 \frac{m}{s}$

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

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

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

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 $x = 990 km$

Question 12: A boy goes to school from his village at 3km/hr and returns back at 2km/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 $x = 6 km$

Question 13: A bus completes a journey of 420 km in $6\frac{1}{2} hr$. The first ¾ 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 $x = 70 \frac{km}{hr}$

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

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 $x = 180 \ km$

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 $x = 60 \ km$

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  $3 \ km$

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 $x = 16 \ km$

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)

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

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

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?

Answer:

Let the train meet at a distance $= x \ km$ from Delhi

$\frac{x}{60}$ $=$ $\frac{(1800-x)}{48}$

Solving for $x = 1000 \ km$. The trains will meet 1000 km from Delhi.

Time taken before them meet $= \frac{1000}{60}$ $= 16$ $\frac{2}{3} hr$

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