5 TIME AND DISTANCE
Speed:
We have the relation between speed, time and distance as follows:
Speed distance/time.
So the distance covered in unit time is called speed.
This forms the basis for Time and Distance. It can be re-written as Distance = Speed X Time or
Time Distance/Speed.
Units of Speed:
The units ofspeed are kmph (km per hour) or m/s.
1 kmph 5/18 m/s
1 m/s= 18/5 kmph
Average Speed:
When the travel comprises of various speeds then the concept ofaverage speed is to be applied.
Average Speed=Total distance covered/Total time oftravel
Note: In the total time above, the time ofrest is not considered.
Example 1:
Ifa car travels along four sides ofa square at 100 kmph, 200 kmph, 300 kmph and 400 kmph tin
average speed.
Soln: Average Speed= Total distance/Total time.
Let each side ofsquare be x km. Then the total distance =
4x km.
The total time is sum of individual times taken to cover each side.
To coverx km at 100 kmph, time =x/ 100.
For the second side time = x/ 200.
Using this we can write average speed= 4x/ (x/100 + x/200 +
x/300+x/400)= 192 kmph.
, Example 2:
A man iftravels at 5/6 th of his actual speed takes 10 min more to travel a distance. Find his usual time.
Soln: Lets bethe actual speed andt be the actual time ofthe man.
Now the speed is (5/6)s and time is (t+10) min. But the distance remains the same.
So distance 1 =
distance 2->s Xt= (5/6)s X (t+10) =>t= 50 min.
Example 3:
Ifa person walks at 30 kmph he is 10 min late to his office.
If he travels at 40 kmph then he reaches to his
office 5 min early. Find the distance to his office.
Soln:
Let the distance to his ofice be d. The difference
between the two timings is given as 15 min =
I /4hr.
Now ifd km are covered at 30 kmph then time d/30.
=
Similarly second time =
d/40.
So, d/30-d/40 1/4=>d=30 km.
Note: When two objects move with speeds sl and s2
(a) In opposite directions their combined
speed =
sl +s2
(b) In same direction their combined
speed =
sl -s2.
Example 4:
Two people start moving from the same point at the same time at 30 kmph and 40 kmph in opposite
directions. Find the distance between them after 3 hrs.
Soln: Speed =
30+ 40 =
70 kmph (since in opposite directions)
Time 3 hrs
So distance =
speed X time =
70 X3 =210 km.
Example 5:
A starts from X to Y at 6 am at 40
kmph and at the sanne time B starts from Yto X at 50 kmph. When will
they meet ifX and Y are 360 km apart'?
Soln: Distance =
360 km
Speed 40+50 90 kmph.
Time =distance/speed= 360/90 4hrs from6 am=> 10 am.
Speed:
We have the relation between speed, time and distance as follows:
Speed distance/time.
So the distance covered in unit time is called speed.
This forms the basis for Time and Distance. It can be re-written as Distance = Speed X Time or
Time Distance/Speed.
Units of Speed:
The units ofspeed are kmph (km per hour) or m/s.
1 kmph 5/18 m/s
1 m/s= 18/5 kmph
Average Speed:
When the travel comprises of various speeds then the concept ofaverage speed is to be applied.
Average Speed=Total distance covered/Total time oftravel
Note: In the total time above, the time ofrest is not considered.
Example 1:
Ifa car travels along four sides ofa square at 100 kmph, 200 kmph, 300 kmph and 400 kmph tin
average speed.
Soln: Average Speed= Total distance/Total time.
Let each side ofsquare be x km. Then the total distance =
4x km.
The total time is sum of individual times taken to cover each side.
To coverx km at 100 kmph, time =x/ 100.
For the second side time = x/ 200.
Using this we can write average speed= 4x/ (x/100 + x/200 +
x/300+x/400)= 192 kmph.
, Example 2:
A man iftravels at 5/6 th of his actual speed takes 10 min more to travel a distance. Find his usual time.
Soln: Lets bethe actual speed andt be the actual time ofthe man.
Now the speed is (5/6)s and time is (t+10) min. But the distance remains the same.
So distance 1 =
distance 2->s Xt= (5/6)s X (t+10) =>t= 50 min.
Example 3:
Ifa person walks at 30 kmph he is 10 min late to his office.
If he travels at 40 kmph then he reaches to his
office 5 min early. Find the distance to his office.
Soln:
Let the distance to his ofice be d. The difference
between the two timings is given as 15 min =
I /4hr.
Now ifd km are covered at 30 kmph then time d/30.
=
Similarly second time =
d/40.
So, d/30-d/40 1/4=>d=30 km.
Note: When two objects move with speeds sl and s2
(a) In opposite directions their combined
speed =
sl +s2
(b) In same direction their combined
speed =
sl -s2.
Example 4:
Two people start moving from the same point at the same time at 30 kmph and 40 kmph in opposite
directions. Find the distance between them after 3 hrs.
Soln: Speed =
30+ 40 =
70 kmph (since in opposite directions)
Time 3 hrs
So distance =
speed X time =
70 X3 =210 km.
Example 5:
A starts from X to Y at 6 am at 40
kmph and at the sanne time B starts from Yto X at 50 kmph. When will
they meet ifX and Y are 360 km apart'?
Soln: Distance =
360 km
Speed 40+50 90 kmph.
Time =distance/speed= 360/90 4hrs from6 am=> 10 am.
