Question

A motorboat whose speed is 18 km/hr in still water. It takes 3 hours more in covering a distance of 72 km upstream than downstream. Find speed of stream

Answer 1

your answer
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Let the speed of the stream be x km/hr.

Speed of the boat upstream = Speed of boat in still water – Speed of the stream

∴ Speed of the boat upstream = ( 18 – x ) km/hr

Speed of the boat downstream = Speed of boat in still water + Speed of the stream

∴ Speed of the boat downstream = ( 18 + x ) km/hr

Time of upstream journey = Time for downstream journey + 3 hr.

•°• $\frac{distance\: covered\: upstream}{speed\: of\: boat\: upstream }$
=
$\frac{distance\: covered\: downstream} {speed\: of\: boat\: downstream}$

=> $\frac{72km}{(18-x)km/h}$=$\frac{72km}{(18+x)km/h}$+3hr

=> 72/18-x = 72/18+x + 3hr

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

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