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Example 22: A cistern has two inlets P and Q which can fill it in 30 minutes and 45 minutes,
respectively. An outlet R can empty the full cistern in 36 minutes. If all three pipes are opened
together in the empty cistern, how much time will it take to fill the cistern completely?

Solution: Time taken by inlet P to fill the cistern = 30 minutes.

1 
So, inlet P fills    30  th part of the cistern in 1 minute.
Time taken by inlet Q to fill the cistern = 45 minutes.
Think and Answer
1 
So, inlet Q fills    45 th part of the cistern in 1 minute. An inlet can fill a water tank

Time taken by outlet R to empty the cistern = 36 minutes in 8 hours. Due to leakage in
a tap, the tank is filled in 10
1 
∴ Outlet R empties  36  th part of the cistern in 1 minute. hours. When the tank is full,

in how much time will it be

So, when they all are opened together, the part of the emptied by the leakage?
cistern to be filled in 1 minute
1 1 1 6 + 4 − 5 5 1
= + − = = =
30 45 36 180 180 36
Thus, when all three pipes are opened together, the cistern will be filled in 36 minutes.

Time and Distance

We know that the speed of a moving object is the distance covered by it in unit time. If an object
covers an equal distance in equal interval of time, then its speed is said to be constant or uniform.
The distance travelled is directly proportional to the time and speed. For a given distance, time
and speed are inversely proportional.
The distance (d), speed (s), and time taken (t) are connected by the following relations:

d d
s = , or t = or d = s × t
t s
Speed is usually expressed in kilometre/hour (km/h) or metre/second (m/s).
5 18
Note that 1 km/h = m/s or 1 m/s = km/h.
18 5
In this section, we mainly focus on the problems related to trains in the following situations:

• Crossing a stationary object with negligible length: When a train crosses a stationary object
whose length is negligible, for example, a tree, a pole, etc., it will cover a distance equal to its
own length.
Example 23: If a train having a length of 360 m, travels at a speed of 54 km/h, then find the time
taken by the train to pass a pole.

Solution: Given, Distance (d) = length of the train = 360 m
5 5
Speed of the train (s) = 54 km/h = 54 × m/s = 15 m/s (Q 1 km/h = m/s)
18 18
d 360 m
So, the time taken by the train to pass a pole = = = 24 s
s 15 m/s

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