What is the speed of the stream?

Given the following statements:

(A) The sum of the time taken by a boat to cover 270 km upstream and downstream is 27 hours.

(B) The speed of the boat downstream is 45 km/h.

(C) The boat covers 90 km upstream in 7 hours.

Which of the following options is correct regarding the sufficiency of the statements to find the speed of the stream?

Question

What is the speed of the stream?

Given the following statements:

(A) The sum of the time taken by a boat to cover 270 km upstream and downstream is 27 hours.

(B) The speed of the boat downstream is 45 km/h.

(C) The boat covers 90 km upstream in 7 hours.

Which of the following options is correct regarding the sufficiency of the statements to find the speed of the stream?

Accepted Answer

**Solution:**

1. Let the speed of the boat in still water be *x* km/h and the speed of the stream be *y* km/h.

2. From statement (A):
   - Time taken upstream = $ \frac{270}{x - y} $
   - Time taken downstream = $ \frac{270}{x + y} $
   - Given sum of times = 27 hours

Therefore, 
   $$\frac{270}{x + y} + \frac{270}{x - y} = 27$$

3. From statement (B):
   - Speed downstream = $ x + y = 45 $ km/h

4. From statement (C):
   - Speed upstream = $ x - y = \frac{90}{7} $ km/h

5. Using any two statements, we can solve for *x* and *y*:
   - Using (A) and (B), substitute $ x + y = 45 $ into (A) to find $ x - y $, then find *y*.
   - Using (A) and (C), substitute $ x - y = \frac{90}{7} $ into (A) to find $ x + y $, then find *y*.
   - Using (B) and (C), directly solve the two equations:
     $$ x + y = 45 $$
     $$ x - y = \frac{90}{7} $$

6. Hence, any two statements are sufficient to determine the speed of the stream.

**Answer:** Any two statements are sufficient to answer the question.

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