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Basic Theory Part 2 for Time and Distance For Upcoming Bank PO n SSC Exam

Posted on - 03-05-2017

QA Math Time And Distance

Bank PO

Problems related to boats and streams are different in the computation of relative speed from those of trains/cars. .

When a boat is moving in the same direction as the water current/stream, the boat is said to be moving WITH THE STREAM OR CURRENT. .

When a boat is moving in a direction opposite to that of the water current/stream, it is said to be moving AGAINST THE STREAM OR CURRENT. .

SPEED OF THE BOAT IN STILL WATER is the speed of the boat when it travels in water that is not moving. .

When the boat is moving upstream, the speed of the water opposes (and hence reduces) the speed of the boat. .

When the boat is moving downstream, the speed of the water aids (and thus adds to) the speed of the boat. Thus, we have .

Speed of the boat against stream = Speed of the boat in still water - Speed of the stream. .

Speed of the boat with the stream = Speed of the boat in still water + Speed of the stream. .

These two speeds, the speed of the boat against the stream and the speed of the boat with the stream, are RELATIVE SPEEDS. .

In problems, instead of a boat, it may be any other moving body, the approach is exactly the same. .

Circular Tracks

When two people are running around a circular track starting at the same time from the same point, we would be interested in finding out the time taken by them to meet for the first time anywhere on the track or to meet for the first time at the starting point. .

This can be done when the two people are running in the same direction or in the opposite direction. .

Similarly, we can find the time taken for THREE people to meet each other to meet for the first time anywhere on the track or at the starting point. .

Let the length of the circular track be L. Let three people be A, B and C run around the circular track with speeds of a, b and c respectively where a > b > c. They start running from the same point at the same time.

Then the following table gives complete details for finding out the time required for each of the various meetings as discussed above. .

Time taken / Situation

Two people A and B running in opposite directions

Two people A and B running in the same direction

Three people A, B and C running in the same direction

To meet for the first time anywhere on the track

LCM of {L/(a - b), L/(b - c)}

To meet for the first time at the starting point

LCM of {L/a, L/b}

LCM of {L/a, L/b}

LCM of {L/a, L/b, L/c}

Also, when two people are running around a circular track starting from the same point at the same time, then every time the two people meet, the faster person covers one full round more than the slower person and vice-versa. .

Some solved example

example.1

Walking at 5 kmph a student reaches his school from his house 15 minutes early and walking at 3 kmph he is late by 9 minutes. What is the distance between his school and his house? .

Solution

Let the distance between school and house be x km. .


&⇒
10x = 30


&⇒
x = 3 km
. .

Example.2

In a 1000 m race, A beats B by 100 m and C by 180 m. In a 1800 m race, by how many meters does B beat C? .

Solution

By the time A covers 1000 m, B covers 1000 - 100 = 900 m and C covers 1000 - 180 = 820 m. .

By the time, B covers 1800 m, the distance C covers = x 820 = 1640

So, B beats C by 1800 - 1640 = 160 m. .

example.3

A man can swim at 6 kmph downstream and 4 kmph upstream. Find the speed of the man in still water and also the speed of the stream. .

Solution

Let the speed of the man in still water be x kmph and speed of the stream be y kmph

x + y = 6 ------- (1) x - y = 4 ----------- (2)

Solving the equations we get x = 5 and y = 1

example.4

A boat travelled from A to B and back to A from B in 5 hours. If the speed of the boat in still water and speed of the stream be 7x5 kmph and lx5 kmph respectively, then what is the distance between A and B? .

Solution

Let distance between A and B be x km

Speed upstream = 7 x 5 – 1 x 5 = 6 kmph

Speed downstream = 7 x 5 + 1 x 5 = 9 kmph

= 5
&⇒
x = 18

example.5

The distance between two persons is 800 m. If they start moving towards each other simultaneously at 10 m/s and 15 m/s, in how much time do they meet? .

Solution

Distance = 800 m

Relative speed = (10 + 15) = 25 m/s

Time taken to meet =

= = 32 sec

 
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