Question

73. A motorboat whose speed is 18 kmph in still water takes 1 hr 30 min
more to go 36 km upstream than to return downstream to the same
spot. Find the speed of the stream.
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Answer 1

Answer:

Speed of boat in still water = 18km/hr

Let speed of the stream = s

Speed of boat upstream = Speed of boat in still water - speed of stream = 18−s

Speed of boat down stream = Speed of boat in still water + speed of stream = 18+s

Time taken for upstream = Time taken to cover downstream + 1

⇒SpeedupstreamDistanceupstream=SpeeddownstreamDistancedownstream+1

⇒18−s24=18+s24+1

⇒24(18+s)=24(18−s)+(18−s)(18+s)

⇒s2+48s−324=0

⇒s2+54s−6s−324=0

⇒(s+54)(s−6)=0

⇒s=6,−54

⇒s=−54

Thus, s=6km/hr, Speed of steam cannot be negative.

Answer 2

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr