Final answer:
The total time for the boat to travel 3000m upstream, wait for 2 minutes, and travel 6000m downstream is approximately 16 minutes and 35 seconds.
Step-by-step explanation:
To solve this problem, we need to calculate the time taken to travel upstream and downstream separately, then sum these times and add the waiting period.
Upstream Travel
Upstream, the boat's effective speed is the difference between the boat's speed and the current's speed. So, the effective speed upstream is 10 m/s - 2 m/s = 8 m/s. To travel 3000 m upstream at 8 m/s, it would take:
Time = Distance / Speed = 3000 m / 8 m/s = 375 seconds.
Waiting Period
The boat waits for 2 minutes which is 2 minutes * 60 seconds/minute = 120 seconds.
Downstream Travel
Downstream, the boat's effective speed is the sum of the boat's speed and the current's speed. Thus, the effective speed downstream is 10 m/s + 2 m/s = 12 m/s. To travel 6000 m downstream at 12 m/s, it would take:
Time = Distance / Speed = 6000 m / 12 m/s = 500 seconds.
Adding up all the times gives us:
Total Time = Upstream Time + Waiting Time + Downstream Time = 375 seconds + 120 seconds + 500 seconds = 995 seconds.
To convert seconds into minutes, we have:
Total Time in Minutes = 995 seconds / 60 = 16.58 minutes, or approximately 16 minutes and 35 seconds.