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DIRECTION for the question: Solve the following question and mark the best possible option.
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 mph, the speed of the stream is :
Let us assume the speed of stream = x mph.
Speed going downstream = 10 + x mph
Speed going upstream = 10 - x mph.
Difference in time taken to cover 36 miles ==> $$\frac{36}{10-x}-\frac{36}{10+x}$$
This is equal to 90 mins = 1.5 hrs.
$$36\left(\frac{1}{10-x}-\frac{1}{10+x}\right)=1.5$$
$$24\left(10+x\ -\ 10+x\right)=\left(10+x\right)\left(10-x\right)$$
$$48x\ =\ 100\ -\ x^2$$
$$x^2+48x-100=0$$
$$\left(x+50\right)\left(x-2\right)=0$$
This gives x = 2 mph.
So, the speed of stream = 2 mph.
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