The document discusses various problems related to time, speed, and distance, including scenarios involving changes in speed affecting arrival times and calculating average speeds for journeys. It presents multiple problem-solving examples involving mathematical relationships between speed, time, and distance, providing step-by-step solutions. Additionally, it includes practice problems for further comprehension and application of these concepts.

1. Time and Distances - 1
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2. 1. Races and Games
2. Problems on Trains
3. Boats and Streams
Time and Distances
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3. Races and Games - 1
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4. 1. A man increases the speed by 25% and reaches his office from his
house 10 min early. Find the time taken by then to reach his office
travelling at his usual speed?
2. A man travels at a speed of 20kmph and reaches his office from his
house 18 min late. If he travels at speed of 25kmph, he reaches 12 min
late. What is the distance between his house and office?
3. A man travels at a speed of 30kmph and reaches his office from his
house, 10min late. If he travels at a speed of 40kmph, he reached 5min
early. What is the speed at which he has to travel to reach on time?
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5. A thief escapes from a prison and starts running at a speed of
6m/s. After 5min, a policeman along with his dog starts chasing
the thief at speeds of 10m/s and 12m/s. What is the distance
travelled by the dog before the policeman catches the thief if it
runs “to and fro” between thief and policeman?
A man travels half of the distance at a speed of 15kmph and the
remaining half at a speed of 10kmph. Find the average speed for
the entire journey?
5.
4.
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6. A man increases the speed by 25% and reaches his office from his house
10 min early. Find the time taken by then to reach his office travelling at
his usual speed?
Ans :
NOTE:
If distance is constant, then speed and time are inversely proportional to each
other.
 s1 : s2 = 100 : 125 => t1 : t2
 4 : 5 => 5 : 4
 1 part = 10 min
 5 parts = 50min
1.
Time taken by then to reach his office travelling at his usual speed = 50min
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7. A man travels at a speed of 20kmph and reaches his office from his
house 18 min late. If he travels at speed of 25kmph, he reaches 12 min
late. What is the distance between his house and office?
2.
Distance between his house and office = 10km.
Ans :
NOTE:
If distance is constant, then speed and time are inversely proportional to each
other.
 s1 : s2 = 20 : 25 => t1 : t2
 4 : 5 => 5 : 4
 1 part = 6 min
 5 parts = 30min = ½ hr
 Distance = 20 * ½ = 10km.
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8. A man travels at a speed of 30kmph and reaches his office from his
house, 10min late. If he travels at a speed of 40kmph, he reached 5min
early. What is the speed at which he has to travel to reach on time?
3.
10 28 = 280
7 40 = 280
Ans :
 s1 : s2 = 30 : 40 => t1 : t2
 3 : 4 => 4 : 3
 1 part = 15 min
 t1 = 60 min => distance = 60min 30kmph = 30km
 time taken at usual speed = 50min
 Speed = = 36kmph
.
speed at which he has to travel to reach on time = 36kmph
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9. A thief escapes from a prison and starts running at a speed of 6m/s. After
5min, a policeman along with his dog starts chasing the thief at speeds of
10m/s and 12m/s. What is the distance travelled by the dog before the
policeman catches the thief if it runs “to and fro” between thief and policeman?
4.
Ans :
 : = 6 : 10
 3 : 5 => : = 5 : 3
 2 part = 5 min = 300 sec.
 1 part = 150 sec
 = = 3 150 sec = 450 sec. => = 450 sec.
 Distance = =
= 5400m
The distance travelled by the dog = 5400mcomsciguide

10. A man travels half of the distance at a speed of 15kmph and the
remaining half at a speed of 10kmph. Find the average speed for the
entire journey?
5.
Ans :
NOTE:
If a man travels two equal distances at speeds of ‘x’ and ‘y’ kmph, then his
average speed for the entire journey is
From the given question… x = 15kmph and y = 10kmph
=> Average speed =
∗ ∗
= 12 kmph.
Average speed for the entire journey = 12 kmph
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11. Same question in different method :
Find out the lcm of the speeds, and assume lcm as total distance and
find the time of the corresponding distances and find the average speed.
Lcm( 10, 15 ) = 30
 Total distance = 30
 t1 = 30/ 15 = 2hr and t2 = 30/10 = 3 hr
 Average speed =
 Avg speed = 60/5 = 12kmph
Average speed for the entire journey = 12 kmph
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Continued…..
Problems for practice are given in the description of the video.
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13. Practice problems
on Races and Games -1
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14. • A man decreases the speed by 40% and reaches his office from his
house 18 min late. Find the time taken by then to reach his office
travelling at his usual speed?
• A man travels at a speed of 40kmph and reaches his office from his
house 20 min late. If he travels at speed of 60kmph, he reaches 10
min late. What is the speed at which he has to travel to reach on
time?
• A man travels half of the distance at a speed of 60kmph, half of the
remaining half at a speed of 30kmph and the remaining distance at a
speed of 10kmph. Find the average speed for the entire journey?
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15. A man decreases the speed by 40% and reaches his office from his
house 18 min late. Find the time taken by then to reach his office
travelling at his usual speed?
Ans :
NOTE:
If distance is constant, then speed and time are inversely proportional to each
other.
 s1 : s2 = 100 : 60 => t1 : t2
 5 : 3 => 3 : 5
 2 part = 18 min
 5 parts = 45min
1.
Time taken by then to reach his office travelling at his usual speed = 45min
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16. A man travels at a speed of 40kmph and reaches his office from his
house 20 min late. If he travels at speed of 60kmph, he reaches 10 min
late. What is the speed at which he has to travel to reach on time?
2.
Distance between his house and office = 10km.
Ans :
NOTE:
If distance is constant, then speed and time are inversely proportional to each
other.
 s1 : s2 = 40 : 60 => t1 : t2
 2 : 3 => 3 : 2
 1 part = 10 min
 2 parts = 20min speed = = 120kmph
 Distance = 1/3 * 60 = 20km.
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17. A man travels half of the distance at a speed of 60kmph, half of the
remaining half at a speed of 30kmph and the remaining distance at a
speed of 10kmph. Find the average speed for the entire journey?
3.
Ans :
lcm ( 60, 30, 10 ) = 60
Now assume the total distance be 60km
 30km at 60 kmph, 15km at 30 kmph, 15km at 10 kmph
 t1 = 30/60 = ½ hr t2 = 15/30 = ½ hr t3 = 15/10 = 3/2 hr
 Average speed =
 Avg speed = = 24kmph
Average speed for the entire journey = 24 kmph
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