A boat covers a certain distance downstream in 90 minutes. If the ratio of the speed of the boat in still water to the speed of the stream is $3:1$, find the time taken by the boat to cover the same distance upstream.

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**Solution:**

1. Let the speed of the boat in still water be $3x$ and the speed of the stream be $x$.

2. Then, the downstream speed = speed of boat + speed of stream = $3x + x = 4x$.

3. The upstream speed = speed of boat - speed of stream = $3x - x = 2x$.

4. Given, time taken downstream = 90 minutes = $\frac{90}{60} = 1.5$ hours.

5. Let the distance be $D$. Using the formula $	ext{Distance} = 	ext{Speed} 	imes 	ext{Time}$,
   $$D = 4x 	imes 1.5 = 6x$$

6. Time taken upstream to cover the same distance:
   $$	ext{Time} = \frac{	ext{Distance}}{	ext{Speed}} = \frac{6x}{2x} = 3 	ext{ hours}$$

**Answer:** 3 hours

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