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