Q. 514.6( 45 Votes )

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

Answer :

Let the speed of stream be x km/h

Speed of boat is 18 km/hr

⇒ Speed of boat in downstream = (18 + x)km/h

⇒ Speed of boat in upstream = (18 – x)km/h

As, 
distance = spped × time

⇒ Time taken by boat in downstream to travel 24 Km =hours

⇒ Time taken by boat in upstream to travel 24 Km  hours
⇒ 

⇒ 

⇒ 

⇒      [using (a + b)(a – b) = a2 – b2]

⇒ 324 – x2 = 48x

⇒ x2 + 48x – 324 = 0

⇒ x2 + 54x – 6x – 324 = 0

⇒ x(x + 54) – 6(x + 54) = 0

⇒ (x + 54)(x – 6) = 0

⇒ x = – 54 or x = 6

(but speed cannot be negative)

⇒ x = 6

Hence the speed of stream is 6 km/h

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