Time and Distance - Arithmetic
Solved Examples: 8
Question (1) An athlete takes 10 second to finish a race of 100 meter. What will his speed in km/h?
Solution
Given, Distance covered (s) = 100 meter
Time taken (t) = 10 second.
Thus, speed (v) in km/h = ?
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v)
⇒ Speed (d) = 10 m/s
Calculation of Speed in km/h
We know that to convert the speed of m/s into km/h, we have to multiply it by 18/5
Thus, speed (d) in km/h
= 2 × 18 = 36 km/h
Thus, speed of the athlete in km/h = 36 km/h Answer
Alternate Method
Alternatively, this type of problem can be solved in the following way:
Since, distance is given in the meter and time is given in the second, and in answer, speed is required in the km/h.
So, first of all, the distance can be converted into kilometers and time into hours, and after that speed can be calculated which will be in kilometers per hour.
Given, distance = 100 m
Now, since 1000 m = 1 km
Thus, 1 m = 1/1000 km
Thus, 100 m
= 1/10 km = 0.1 km
⇒ 100 m = 0.1 km
Thus, distance in km = 0.1 km
As given, time = 10 second
We know that, 1 hour = 3600 second
Thus, 1 second = 1/3600 second
Thus, 10 second
⇒ 10 second = 1/360 hour
Thus, time (t) = 1/360 hour
Now, we know that, speed (v) = Distance/Time
= 36 km/h
Thus, speed in km/h = 36 km/h Answer
Question (2) An athlete takes 10 second to finish a race of 150 meter. What will his speed in km/h?
Solution
Given, Distance covered (s) = 150 meter
Time taken (t) = 10 second.
Thus, speed (v) in km/h = ?
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v) = 150 m / 10 s
⇒ Speed (d) = 15 m/s
Calculation of Speed in km/h
We know that, to convert the speed of m/s into km/h, we have to multiply it with 18/5
Thus, speed (d) in km/h
= 3 × 18 = 54 km/h
Thus, speed of the athlete in km/h = 54 km/h Answer
Alternate Method
Alternatively, this type of problem can be solved in the following way:
Since, distance is given in the meter and time is given in the second, and in answer speed is required in the km/h.
So, first of all, the distance can be converted into kilometer and time into hour, and after that speed can be calculated which will be in kilometer per hour.
Given, distance = 150 m
Now, since 1000 m = 1 km
Thus, 1 m = 1/1000 km
Thus, 150 m = 150/1000 km
Thus, distance in km = 15/100 km
As given, time = 10 second
We know that, 1 hour = 3600 second
Thus, 1 second = 1/3600 second
Thus, 10 second = 10/3600 hour
⇒ 10 second = 1/360 hour
Thus, time (t) = 1/360 hour
Now, we know that, speed (v) = Distance/Time
= 3 ⇒ 18 km/h
= 54 km/h
Thus, speed in km/h = 54 km/h Answer
Question (3) A man takes 10 minute to cross a bridge of 300 meter. What will be his speed in km/h and m/s?
Solution
Given, Distance covered (s) = 300 meter
Time taken (t) = 10 minute
= 10 ⇒ 60 second
Thus, time (t) = 600 second
Thus, speed (v) in km/h and m/s = ?
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v) = 300 m / 600 s
⇒ Speed (d) = 1/2 m/s or 0.5 m/s
Calculation of Speed in km/h
We know that, to convert the speed of m/s into km/h, we have to multiply it with 18/5
Thus, speed (d) in km/h
= 1.8 km/h
Thus, speed of the man in meter per second = 1/2 m/s or 0.5 m/s Answer
Thus, speed of the man in km/h = 36 km/h Answer
Question (4) A man takes 15 second to run around a square field. If the side of the field is 15 meter. What will be his speed in km/h and m/s?
Solution
Given, Side of the square field = 15 meter
Time taken to run around the given field (t) = 15 second
Thus, speed (v) in m/s and km/h = ?
Here, since the man is running around a square field, this means distance will be equal to perimeter of the given square field.
Calculation of perimeter of the given square field
We know that, perimeter of a square = Side × 4
Thus, perimeter of the given square field = 15 m × 4
= 60 m
Thus, distance covered = perimeter of the square field = 60 m
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v) = 60 m / 15 s
⇒ Speed (d) = 4 m/s
Thus, speed in meter per second = 4 m/s
Calculation of Speed in km/h
We know that, to convert the speed of m/s into km/h, we have to multiply it with 18/5
Thus, speed (d) in km/h
= 14.4 km/h
Thus, speed of the man in meter per second = 4 m/s Answer
Thus, speed of the athlete in km/h = 14.4 km/h Answer
Question (5) A man takes 20 second to run around a square field. If the side of the field is 25 meter. What will be his speed in km/h and m/s?
Solution
Given, Side of the square field = 25 meter
Time taken to run around the given field (t) = 20 second
Thus, speed (v) in m/s and km/h = ?
Here, since the man is running around a square field, this means distance will be equal to perimeter of the given square field.
Calculation of perimeter of the given square field
We know that, perimeter of a square = Side × 25
Thus, perimeter of the given square field = 25 m × 4
= 100 m
Thus, distance covered = perimeter of the square field = 100 m
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v) = 100 m / 20 s
⇒ Speed (d) = 5 m/s
Thus, speed in meter per second = 5 m/s
Calculation of Speed in km/h
We know that, to convert the speed of m/s into km/h, we have to multiply it with 18/5
Thus, speed (d) in km/h
= 18 km/h
Thus, speed of the man in meter per second = 5 m/s Answer
Thus, speed of the athlete in km/h = 18 km/h Answer
Question (6) A man takes 20 second to run around a rectangular field. If the length and width of the field are 40 meter and 20 meter respectively, then what will be the speed of man in km/h and m/s?
Solution
Given, length of the rectangular field = 40 meter
And width of the rectangular filed = 20 meter
Time taken to run around the given field (t) = 20 second
Thus, speed (v) in m/s and km/h = ?
Here, since the man is running around a rectangular field, this means distance will be equal to perimeter of the given square field.
Calculation of perimeter of the given rectangular field
We know that, perimeter of a rectangle = 2(Length × Width)
Thus, perimeter of the given rectangular field = 2 (40 m × 20 m)
= 2 × 60 m
= 120 m
Thus, distance covered = perimeter of the rectangular field = 120 m
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v) = 120 m / 20 s
⇒ Speed (d) = 6 m/s
Thus, speed in meter per second = 6 m/s
Calculation of Speed in km/h
We know that, to convert the speed of m/s into km/h, we have to multiply it with 18/5
Thus, speed (d) in km/h
= 21.6 km/h
Thus, speed of the man in meter per second = 6 m/s Answer
Thus, speed of the athlete in km/h = 21.6 km/h Answer
Question (7) A man takes 30 second to run around a rectangular field. If the length and width of the field are 10 meter and 5 meter respectively, then what will be the speed of man in km/h and m/s?
Solution
Given, length of the rectangular field = 30 meter
And width of the rectangular filed = 5 meter
Time taken to run around the given field (t) = 30 second
Thus, speed (v) in m/s and km/h = ?
Here, since the man is running around a rectangular field, this means distance will be equal to perimeter of the given square field.
Calculation of perimeter of the given rectangular field
We know that, perimeter of a rectangle = 2(Length × Width)
Thus, perimeter of the given rectangular field = 2 (10 m × 5 m)
= 2 × 15 m
= 30 m
Thus, distance covered = perimeter of the rectangular field = 30 m
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v) = 30 m / 30 s
⇒ Speed (d) = 1 m/s
Thus, speed in meter per second = 1 m/s
Calculation of Speed in km/h
We know that, to convert the speed of m/s into km/h, we have to multiply it with 18/5
Thus, speed (d) in km/h
= 3.6 km/h
Thus, speed of the man in meter per second = 1 m/s Answer
Thus, speed of the athlete in km/h = 3.6 km/h Answer
Question (8) A man takes 1 minute to run around a rectangular field. If the length and width of the field are 50 meter and 40 meter respectively, then what will be the speed of man in km/h and m/s?
Solution
Given, length of the rectangular field = 50 meter
And width of the rectangular filed = 40 meter
Time taken to run around the given field (t) = 1 minute
= 60 second
Thus, speed (v) in m/s and km/h = ?
Here, since the man is running around a rectangular field, this means distance will be equal to perimeter of the given square field.
Calculation of perimeter of the given rectangular field
We know that, perimeter of a rectangle = 2(Length × Width)
Thus, perimeter of the given rectangular field = 2 (50 m × 40 m)
= 2 × 90 m
= 180 m
Thus, distance covered = perimeter of the rectangular field = 180 m
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v) = 180 m / 30 s
⇒ Speed (d) = 6 m/s
Thus, speed in meter per second = 6 m/s
Calculation of Speed in km/h
We know that, to convert the speed of m/s into km/h, we have to multiply it with 18/5
Thus, speed (d) in km/h
= 21.6 km/h
Thus, speed of the man in meter per second = 6 m/s Answer
Thus, speed of the athlete in km/h = 21.6 km/h Answer
Question (9) A cyclist takes 1.5 minute to run around a rectangular field. If the length and width of the field are 60 meter and 30 meter respectively, then what will be the speed of man in km/h and m/s?
Solution
Given, length of the rectangular field = 60 meter
And width of the rectangular filed = 30 meter
Time taken to run around the given field (t) = 1.5 minute
= 1.5 × 60 second
= 90 second
Thus, speed (v) in m/s and km/h = ?
Here, since the man is running around a rectangular field, this means distance will be equal to perimeter of the given square field.
Calculation of perimeter of the given rectangular field
We know that, perimeter of a rectangle = 2(Length × Width)
Thus, perimeter of the given rectangular field = 2 (60 m × 30 m)
= 2 × 90 m
= 180 m
Thus, distance covered = perimeter of the rectangular field = 180 m
We know that, speed (v) = Distance (s)/Time (t)
Thus, Speed (v) = 180 m / 90 s
⇒ Speed (d) = 2 m/s
Thus, speed in meter per second = 2 m/s
Calculation of Speed in km/h
We know that, to convert the speed of m/s into km/h, we have to multiply it with 18/5
Thus, speed (d) in km/h
= 7.2 km/h
Thus, speed of the man in meter per second = 2 m/s Answer
Thus, speed of the athlete in km/h = 7.2 km/h Answer
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