If a boat travels 54 km…

Physics Questions

If a boat travels 54 km downstream in 9 hours and 50 km upstream in 10 hours, how long will it take to travel 55 km in still water? A. 4 hours 40 minutes B. 5 hours 20 minutes C. 5 hours 45 minutes D. 6 hours 10 minutes

Short Answer

The boat’s downstream speed is 6 km/h and upstream speed is 5 km/h, giving an average speed of 5.5 km/h in still water. To travel 55 km at this speed, the time taken is 10 hours, which converts to 6 hours and 10 minutes.

Step-by-Step Solution

Determine Boat Speeds

To calculate the time taken by the boat to travel in still water, we first need to find the boat’s speed in both downstream and upstream currents. We have:

  • Downstream speed: 54 km in 9 hours = 6 km/h
  • Upstream speed: 50 km in 10 hours = 5 km/h

Calculate Average Speed

Next, we calculate the average speed of the boat in still water. Since the downstream speed is greater than the upstream speed, we can determine the still water speed by averaging the two speeds:

  • Average speed = (6 km/h + 5 km/h) / 2 = 5.5 km/h

Calculate Time to Travel Distance

Finally, we use the average speed to find out how long it takes to travel a distance of 55 km in still water. We apply the formula for time:

  • Time = Distance / Speed = 55 km / 5.5 km/h = 10 hours

Converting 10 hours results in 6 hours and 10 minutes as the final answer.

Related Concepts

Downsstream speed

The speed of the boat when traveling with the current, calculated by dividing the distance covered by the time taken.

Upstream speed

The speed of the boat when traveling against the current, determined by the distance traveled divided by the time taken.

Average speed

The mean speed of the boat in still water, calculated by taking the average of the downstream and upstream speeds.

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