A boat takes 90 minutes less to travel 36 mil | vedclass

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(A) Let the speed of the stream be $x$ miles/hour.Speed of the boat in still water = $10$ miles/hour.Downstream speed = $(10 + x)$ miles/hour.Upstream

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$2$

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(A) Let the speed of the stream be $x$ miles/hour.Speed of the boat in still water = $10$ miles/hour.Downstream speed = $(10 + x)$ miles/hour.Upstream speed = $(10 - x)$ miles/hour.Time taken to travel $36$ miles upstream = $\frac{36}{10 - x}$ hours.Time taken to travel $36$ miles downstream = $\frac{36}{10 + x}$ hours.Given that the difference in time is $90$ minutes,which is $\frac{90}{60} = 1.5$ hours.Therefore,$\frac{36}{10 - x} - \frac{36}{10 + x} = 1.5$.$\frac{36(10 + x) - 36(10 - x)}{(10 - x)(10 + x)} = 1.5$.$\frac{360 + 36x - 360 + 36x}{100 - x^2} = 1.5$.$\frac{72x}{100 - x^2} = 1.5$.$72x = 1.5(100 - x^2)$.$72x = 150 - 1.5x^2$.$1.5x^2 + 72x - 150 = 0$.Dividing by $1.5$,we get $x^2 + 48x - 100 = 0$.$(x + 50)(x - 2) = 0$.Since speed cannot be negative,$x = 2$ miles/hour.

$A$ boat takes $90$ minutes less to travel $36$ miles downstream than to travel the same distance upstream. If the speed of the boat in still water is $10$ miles/hour,the speed of the stream is.......miles/hour.

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