A boat takes 2 hours to travel from point A to point B in still water. To determine the speed of the boat upstream, which of the following pieces of information are necessary?

A. Distance between points A and B.

B. Time taken to travel downstream from point B to point A.

C. Speed of the stream current.

Which of the following options is correct?

Question

A boat takes 2 hours to travel from point A to point B in still water. To determine the speed of the boat upstream, which of the following pieces of information are necessary?

A. Distance between points A and B.

B. Time taken to travel downstream from point B to point A.

C. Speed of the stream current.

Which of the following options is correct?

Accepted Answer

**Solution:**

1. Let the distance between points A and B be *d*.

2. Let the speed of the boat in still water be *x* km/h.

3. Let the speed of the stream current be *y* km/h.

4. Given that the boat takes 2 hours to cover distance *d* in still water, we have:
   $$\frac{d}{x} = 2$$

5. To find the upstream speed, which is *x - y*, we need to know the values of *x* and *y* or be able to calculate them.

6. The information given in options:
   - A: Distance *d* is known.
   - B: Time taken downstream from B to A, which is $$\frac{d}{x + y}$$.
   - C: Speed of the stream *y*.

7. Using any two of these three pieces of information, we can find the upstream speed:
   - If A and B are known, we can find *x* and *y* by solving equations.
   - If B and C are known, we can find *x* and then calculate upstream speed.
   - If A and C are known, we can find *x* from the still water speed and then calculate upstream speed.

Therefore, any pair among A and B, B and C, or C and A is sufficient to determine the upstream speed.

**Answer:** (b) Any one pair among A and B, B and C, or C and A is sufficient

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