Q23 of 30 Page 1

A motor boat whose speed is 18 km/hr in still water takes 1hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

OR


A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/ hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original average speed?

Let Speed of the stream be x km/h

Formula Used:

Going Upstream: 

Speed = Speed of boat in still water - speed of stream
Speed = (18 - x) km/h
Distance = 24 km



Going Downstream:

Speed = Speed of boat in still water + speed of stream
Speed = (18 + x) km/h
Distance = 24 km


According to the question,


Time taken Upstream = Time taken downstream + 1hr





⇒ x2 + 48x – 324 = 0


⇒ x2 + 54x – 6x – 324 = 0


⇒ x(x + 54) – 6(x + 54) = 0


⇒ (x – 6)(x + 54) = 0


⇒ X = 6 or – 54


Since “x” is the time, it has to be non negative


∴ x = 6 km/h


So, the speed of the stream is 6km/h


OR


Let Original Average Speed be x km/h



According to the question, the total time taken is 3 hrs


⇒


⇒


⇒ 3x2 – 117x – 378 = 0


⇒ x2 – 39x – 126 = 0


⇒ x2 – 42x + 3x – 126 = 0


⇒ x(x – 42) + 3(x – 42) = 0


⇒ (x + 3)(x – 42) = 0


⇒ x = – 3 or 42


As “x” is speed, it has to be non negative


∴ x = 42 km/h


So, the original average speed is 42 km/h.

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