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í∫’®Ω’¢√®Ωç 15 -ÅéÓd-•®Ω’ 2009
TIME AND DISTANCE
The
relation among distance, time and speed
is
Distance = Speed × Time.
Speed
Time
Distance
Time
⎯
=
=
Distance
⎯
Speed
If a car covers 40 kilometres in each hour
then the speed of the car is 40 kmph.
If a man travels 15 metres in one second's
time then the speed of the man is 15 mps.
e.g.: A car covers a distance of 1450 kms. in
25 hours. What is the speed of the car?
(SBI 2008)
A) 58 kms./ hr. B) 66 kms./ hr.
C) 72 kms./ hr. D) Cannot be determined
E) None of these
Ñ-Ø√-úø’ £j«-ü¿®√-¶«-ü˛
2xy
Sol: average speed = ⎯
x+y
2 × 80 × 120
⇒
2
BOATS AND
STREAMS
⎯⎯
80 + 120
= 96 kmph
TRAINS
If a train has to cross a pole or a man or any
particular point then it has to cover a distance
equal to its own length.
If a train has to cross a platform or bridge or
tunnel etc. then it has to cover a sum of the
length equal to its length and platform/ bridge/
tunnel length.
Relative speed
When two speeds are in opposite direction,
Relative speed = sum of the speeds.
When two speeds are in the same direction,
Relative speed = difference of the speeds.
Still water: Water
without motion. A
boat can travel or a
man can swim in
that water with their
original speeds.
Stream/ current: Water flow with some
speed.
Down stream:
Along with the flow .=
Speed of the Boat + Speed of the current
Upstream: Against the water flow =
Speed of the Boat - Speed of the current
If the speed of the boat in still water is 'b'
kmph and speed of the current is 'c' kmph
respectively, then
What is the speed of the car?
Sol:
Distance
⎯
Speed =
Time
1450 km
= 58 kmph
25 hours
Hence, the answer is (A).
Conversion of speeds:
KMPH to MPS
Kilometre
1000 Metres
⎯ = ⎯⎯
hour
3600 Seconds
5
⇒ ⎯ mps
18
5
Hence 1 kmph = ⎯ mps
18
MPS to KMPH
18
1 mps = ⎯ kmph
5
e.g.: 35 mps is how many kmph?
18
Sol: 35 × ⎯ = 126 kmph
5
e.g.: In what time can a man cover 360 metres
at a speed of 72 kmph?
A) 5 hours
B) 12 sec
C) 18 sec
D) 5 sec
E) None of these
Sol: Distance = 360 m, Speed = 72 kmph
5 = 20 mps
= 72 × ⎯
18
Distance
360m
Time = ⎯ = ⎯ = 18 Sec
Speed
20 mps
Hence the answer is (C).
Note: When two equal distances are covered
with two different speeds (x, y), then the
2xy
average speed = ⎯
x+y
e.g.: A car covers 175 km at an average speed
of 80kmph and another175km at an average speed of 120kmph. Find the average
speed of the car for the entire distance.
Downstream (DS) = b + c
Upstream (US)
= b-c
Q.APTITUDE
⇒ ⎯
EXERCISE
1. A bus covers a distance of 2,924 kms. in 43
hours. What is the speed of the bus ?
(SBI 2008)
A) 72 kms./hr. B) 60 kms./hr.
C) 68 kms./hr. D) Cannot be determined
E) None of these
2. A man covers a distance of 160 km at 90
km/hr and next 160 km at 60 km/hr. What is
his average speed for his whole journey of
320 km?
A) 75 kmph B) 68 kmph
C) 72 kmph
E) 85 kmph E) None of these
3. A 275 m long train running at 60 kmph
crosses a platform in 36 sec. Find the
length of the platform.
A) 250 m
B) 275 m
C) 325 m
D) 450 m
E) None of these
4. A boat covers 162 km upstream in 6 hours.
If the speed of the current of the stream is
3 kmph, find the speed of the boat.
A) 30 kmph B) 24 kmph
C) 32 kmph
D) 18 kmph E) None of these
DS + US
= ⎯
2
DS - US
Speed of the current (c) = ⎯
2
e.g.: A boat covers 92 km downstream in 4
hours. If the speed of the boat is 19kmph,
find the speed of the current.
A) 2 kmph
B) 5 kmph
C) 8 kmph
D) 4 kmph
E) None of these
92km
Sol: Speed = ⎯ = 23 kmph
4hrs
Boat + Current = 23 ⇒ 19+ Current = 23
∴ Current = 23 -19 = 4 kmph.
Hence, the answer is (D).
Speed of the boat (b)
e.g.: 1: In what time a
125 m long train
running at 90
kmph can cross
a signal pole?
A) 1.3 sec
B) 5 sec
D) 15 sec
G.S.GIRIDHAR
C) 12 sec
E) None of these
Sol: Distance = 125m, speed = 90 kmph
5
= 90 × ⎯ = 25 mps
18
Distance
125m
Time = ⎯ = ⎯ = 5 Sec.
Speed
25 mps
Hence, the answer is (B).
e.g.: 2: A 250 m long train running at 72kmph
speed crosses a bridge in 19sec. Find
the length of the bridge.
A) 150m
B) 225m
D) 175m
E) None of these
C) 130m
Sol: Let the length of the bridge be 'x' meters
Distance = (250 + x)m, speed = 72 kmph
5
= 72 × ⎯ = 20 mps
18
Speed = 19 sec.
Distance = speed × time
250 + x = 20 mps × 19 sec
250 + x = 380 m
⇒ x = 130 m Hence, the answer is (C).
5. Speed of a boat is 8 kmph. It goes to a distance from A to B upstream and comes
back from B to A downstream in 24 hours.
If the speed of the current is 2 kmph, find
the distance between A and B.
A) 60 km
B) 75 km
C) 40 km
D) 90 km
E) None of these
ANSWERS 1) D 2) C 3) C 4) A 5) D
EXPLANATIONS
2924 km
1. Speed = ⎯ = 68 kmph
43 hrs
2xy
2 × 60 × 90
2. Average speed = ⎯ ⇒ ⎯
x+y
60 + 90
= 72 kmph
3. Let the length of the platform be 'x' km.
5
275 + x = 60 × ⎯ × 36 ⇒ x = 325m
18
162 km
4. speed = ⎯ = 27 kmph
6 hrs
upstream = 27 kmph
Boat - Current = 27 kmph
Boat - 3 = 27 ⇒ Boat = 30 kmph.
5. Let the distance between A and B be 'x' km.
x
x = 24 ⇒ x = 90km.
∴ ⎯
+ ⎯
8-2
8+2
SOME MORE MODELS
1. A train 100 metre long is running at the
speed of 21 km/hr and another train 150
meter long is running at the speed of 36
km/hr in the same direction. How long will
the faster train take to pass the first train?
Sol: Sum of the length of both the train
= 100 + 150 = 250 m
Difference of their speeds = 21 - 36
(same direction)
5
25
= 15 km/hr = 15 × ⎯ m/sec = ⎯ m/sec
18
6
250
⎯
25
required time = ⎯ = 60 seconds
6
2. A person going in a car at 30 kmph reaches
his office t1 minutes late. If he goes at
40kmph he reaches there t2 minutes earli-
er. How far is the office from his house?
Note: A person walking at x km/hr reaches his
office t1 minutes late. If he walks at
y km/hr, he reaches there t2 minutes
earlier, then
The distance of the office from his house =
x × y t1 + t2
⎯ × ⎯ km
60
y-x
Sol: Required distance =
40 × 30
5+10
⎯ × ⎯ km.
40 - 30
60
15
40 × 30
= ⎯ × ⎯ km. = 30km.
10
60
3. A car takes 5 hours to cover a distance of
300 km. how much should the speed in
km/hr be maintained to cover the same dis4
tance in ⎯
of the previous time?
5
4
Sol. Distance = 300 km
Time = ⎯
th of 5
5
= 4 hours
Distance = ⎯
300
Required speed = ⎯
Time
4
= 75 km/hr
4. In what time a 350m long train running at
108 kmph speed can overtake a 175 m long
train running at 36 kmph speed?
A) 26.25 sec B) 12.5 sec C) 21.75 sec
D) 32.15 sec E) None of these
Sol: Distance 350 + 175 = 525 m
Speed = 108 - 36 = 72 kmph
5 = 20 mps
= 72 × ⎯
18
525 m
Time = ⎯ = 26.25 Sec.
20 mps
Hence, the answer is (A).
5. A boat covers 90 km down stream or 66 km
upstream in the same time. If the speed of the
current is 2 kmph, find the speed of the boat.
A) 18 kmph B) 13 kmph C) 11 kmph
D) 9 kmph
E) None of these
Sol: Let the speed of the boat be 'x' kmph
Time to cover 90 km downstream
90 km
= ⎯
(x+2) kmph
Time to cover 66 km upstream
66 km
= ⎯
(x - 2) kmph
but the time to cover both the distances is same
90
66
⎯ = ⎯ ⇒ x = 13 kmph
x +2
x-2
Hence, the answer is (B).
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