A boat goes to a place and return back in 45 hours. It can go 10 km upstream in 1 hour and 20 km downstream in the same time. Find the total distance covered by the boat in the whole journey.

Solution

Given:
– The boat goes to a place and returns back in 45 hours.
– The speed of the boat upstream is 10 km/hour.
– The speed of the boat downstream is 20 km/hour.

Let the distance between the starting point and the destination be \(x\) km.

Time Taken for the Journey:

– Time taken to go upstream (to the destination) = \(\frac{x}{10}\) hours
– Time taken to go downstream (return) = \(\frac{x}{20}\) hours
– Total time for the round trip = \(\frac{x}{10} + \frac{x}{20}\) hours

Given that the total time for the round trip is 45 hours, we can write:
\[ \frac{x}{10} + \frac{x}{20} = 45 \]

Multiplying all terms by 20 to clear the denominators:
\[ 2x + x = 900 \]
\[ 3x = 900 \]
\[ x = 300 \]

Total Distance Covered:

The total distance covered by the boat in the whole journey (going and returning) is:
\[ 2 \times x = 2 \times 300 = 600 \text{ km} \]

Conclusion

The total distance covered by the boat in the whole journey is 600 km.