Time, Distance and Speed
FORMULA(Problem on Time, Distance & Speed )
i) `Time=(Distance)/(speed)`
ii) Distance = Speed X Time
Distance
iii) Speed = ---------------
Time
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iv) `x km/hr` = x X ---- m/sec
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v) y m/sec = y X----- km/hr
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vi) If a certain distance is covered at x km/hr and the same distance is covered at y km/hr , then the average speed during whole journey = 2xy/(x+y) km/hr.
vii) If a man changes his speed in the ratio m:n, then the ratio of times takes becomes n:m.
Example on Time and Distance :
1) Express 63 km/hr into metres/sec .
Solution :
5
63 km/hr = 63 X -------m/sec = 17.5 m/sec.
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2) Colambus travels distances of 2500 km , 1200 km and 500 km at the rate of 500 km/hr, 400 km/hr and 250 km/hr respectively. Find the average speed .
Solution :
Total distance = ( 2500 + 1200 + 500 )km = 4200 km
2500 1200 500
Total time taken = -------- + -------- + --------- hrs = 10 hrs.
500 400 250
4200
Average Speed = --------- km/hr = 420 km/hr.
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3) A distance is covered in 3 hours 48 min. at 5 kmph. How much time will be taken to cover it at 28.5 kmpl ?
Solution :
Distance = (speed X Time )
= 5 X 19/5 km
= 19 km.
Distance
Time = -----------------
speed
19
= ------ hrs.
28.5
19
= ---------X 60 min.
28.5
= 40 min.
Formula ( Boats & streams )
1) Let the speed of a boat in still water be x km/hr and let the speed of the steram be y km/ hr. Then :
i) Speed downstream = ( x + y)km/hr
ii) Speed upstream = ( x - y ) km/hr.
2) Let speed downstream = u km/hr & speed upstream = v km/hr.
Then, 1
i) Rate in still water = ------ ( u + v)km/hr
2
1
ii) Rate of current = ------- ( u - v )km/hr
2
Example on Boats & Streams
1) A woman can row 6 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream .
Solution :
Let woman's rate upstream = x km/h .
then, woman's rate downstream = 2x km/h
1
woman's rate in still water = ---------( x + 2x )km/h
2
6 = 3x/2
Rate upstream x = 4 km/h
Rate downstream 2x = 8 km/h
Rate of current 1 X ( 8 - 4 )
= ------------------km/h = 2 km/h
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2)In a stream running at 2 km/h, a boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of the boat in still water .
Solution :
Let the speed of boat in still water be x km/h
Speed downstream = ( x + 2 )km/h,
Speed upstream = ( x - 2 ) km/h,
10 10 55
-------- + ------- = -----
x - 2 x + 2 60
11x^2 - 240x - 44 = 0
( x -22 ) ( 11x + 2 ) = 0
x = 22.
Rate in still water = 22 km/h
Formula ( Trains )
i) Time taken by a train x metres long in passing a signal post or a pole or a standing man is the same as the time taken by the train to cover x metres with its own speed .
ii) Time taken by a train x metres long in passing a stationary object of length y metres is the same as the time taken by the train to cover ( x + y ) metres with its own speed .
iii) Suppose two trains or bodies are moving in th e same direction at u km/h. If two train of lengths x km and y km move in the same direction at u km/h and v km/h ( where u > v ), then time taken to cross each other = ( x + y )/ ( u - v ) hrs .
iv) Suppose two trains or bodies are moving in the opposite directions at u km/h and v km/h. Then, relative speed = (u + v ) km/h . If two trains x km and y km move in the opposite directions at u km/h and v km/h, then time taken to cross each other = ( x + y )/ ( u + v ) hrs .
v) If two trains start at same time from A and B towards each other and after crossing. they take a & b hours in reaching B and a respectively. Then ,
A's speed : B's speed = ( √b : √a ).
Example on Trains
1) A train 160 m long is running with a speed of 48 km/h. In what time will it pass a fencing pole ?
Solution :
5 40
Speed of train = 48 X --------m/sec. = --------m/sec
18 3
Distance 3
Passing Time to the pole = ------------- =160 X --------sec = 12 sec.
Speed 40
2) A woman is standing on a railway bridge which is 50 m long. He finds that a train crosses the bridge
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in 4------ seconds but himself in 2 seconds. Find the length of train and its speed .
2 just
Solution :
Let the length of train be x metres,
then, the train covers x metres in 2 seconds and
1
( x + 50 ) m in 4---- = ( 9/2 ) seconds.
2
x x + 50
length of train ------ = -------------
2 9/2
9 x = 4 ( x + 50 )
9 x = 4 x + 200
9 x - 4 x = 200
5 x = 200
x = 40
Distance 40 18
Speed = ------------- m/sec = ---------m/sec. = 20 m/sec. = 20 X --------- km/m.
time 2 5
= 72 km/m.
Exercise
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1) If a person travels 10------- km in 3 hours , then the distance covered by him in 5 hours will be :
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a) 18 km b) 17 km c) 16 km d) 15 km
2) A boy goes to the school with the speed of 3 km/h and returns with the speed of 2 km/h. If he takes 5 hours in all , then the distance ( in kms ) between the village and the school is :
a) 6 b) 7 c) 8 d) 9
3) A student walks from his house at 5 km/h and reaches his school 10 minutes late. If his speed had been 6 km/h he would have reached 15 minutes early . The distance of his school from his house is :
a) 2.5 km b ) 12.5 km c) 5.5 km d) 3.6 km
4) If a train 110 m long passes a telephone pole in 3 seconds, then the time taken ( in seconds ) by it to cross a railway platform 165 m long , is :
a) 3 b) 4 c) 5 d) 7.5
5) A train 700 m long is running at the speed of 72 km/h. If it crosses a tunnel in 1 minute, then the length of tunnel ( in metres ) is :
a) 700 m b) 600 m c) 550 m d) 500 m
6) If a 200 m long train crosses a platform of the same length as that of the train in 20 seconds, then the speed of the train is :
a) 70 km/h b) 50 km/h c) 72 km/h d) 82 km/h
7) A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long. The length of the train ( in metres ) is :
a) 73 m b) 85 m c) 90 m d) 100 m
8) Two trains of lengths 120 m and 80 m are running in the same direction with velocities of 40 km/h and 50 km/h respectively. The time taken by then to cross each other , is :
a) 65 sec b) 72 sec c) 78 sec d) 90 sec
9) Two trains whose lengths are 180 m and 220 m respectively are running in direction opposite to one another with respectively speeds of 40 km/h and 50 km/h. Time taken by them in crossing one another will be :
a) 16 sec b ) 12 sec c) 15 sec d) 23 sec
10) A boat takes 2 hours to travel a distance of 9 km down the current and it takes 6hoursw to travel the same distance against the current. The speed of the boat in still water and that of the current . The speed of the boat in still water and that of the current ( in km/h ) respectively are :
a) 4, 1.2 b) 4, 5 c) 3.5 , 2.5 d) 4, 2
Answer
1) b 2) a 3) b 4) d 5) d 6) c 7) c 8) b 9) a 10) c
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