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

i) km/hr ii) km/hr iii) km/hr iv) km/hr

Answer:

i)

ii)

iii)

iv)

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

i) m/sec ii) m/sec iii) m/sec iv) m/sec

Answer:

i)

ii)

iii)

iv)

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

Answer:

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

Answer:

Distance covered walking

Time to cover 10 km on cycle or 50 minutes

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

Answer:

Distance covered by the car

Speed to cover the same distance in 8 hr

Hence the speed must be increased by

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

Answer:

Distance covered by the bus

Speed to cover the same distance in 40 min

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

Answer:

Speed at the start

Distance covered in first 2 hours

Speed After 2 hours

Distance covered in 3rd and the 4th hour

Total distance covered by end of 4th hours

Distance left to be covered after end of 4th hour

Speed After 4 hours

Time taken to cover 45 km at speed of

Hence the total time to cover

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

Answer:

Length of one step

Distance covered in 1 sec

- i) Speed in
- ii) Speed in

Question 9: A man walks at km/hr for hours and at km/hr for hours. Find his average speed.

Answer:

Average Speed

Average Speed

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

Answer:

Average Speed

Average Speed

Question 11: Two buses travel to a place at km/hr and km/hr respectively. If the second bus takes hours less than the first for the same journey, find the length of the journey.

Answer:

Let be the distance of the journey

Time taken by the First bus

Time taken by the Second bus

Therefore

Solving for

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

Answer:

Let be the distance of the journey

Time taken to reach school

Time taken return from

Therefore

Solving for

Question 13: A bus completes a journey of km in . The first part of the journey performed at km/hr. Calculate the speed of the rest of the journey.

Answer:

Let be the speed of the rest of the journey

Solving for

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

Answer:

Average Speed

Average Speed

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

Answer:

Let be the distance of the journey.

Solving for

Question 16: A cyclist covered a certain distance in hours. The speed for first half of the distance was km/hr and for the second half it was km/hr. Find the total distance covered by him.

Answer:

Let be the distance of the journey.

Solving for

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

Answer:

Let be the distance of each leg

Solving for and the total distance is

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

Answer:

Let be the distance traveled by foot

Solving for

Question 19: Rohan cycles to his office at the rate of km/hr and is late by minutes. However, if he travels at km/hr, he reaches minutes earlier than the usual time. What is the distance of his office from his residence?

Answer:

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

Solving for (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 km/hr. However, he will reach there at 12 noon if he travels at km/hr. At what speed must he travel to reach A at 1 p.m.?

Answer:

Let the distance traveled

Solving for

Solving for

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

Answer:

Let the distance traveled by the train

Solving for (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 km. A train leaves Delhi and proceeds towards Hyderabad at a uniform speed of km/hr. Another train leaves Hyderabad at the same time and proceeds towards Delhi at a uniform speed of km/hr. When and where will they meet?

Answer:

Let the train meet at a distance from Delhi

Solving for . The trains will meet 1000 km from Delhi.

Time taken before them meet