Final answer:
By setting equations for the distances traveled by both boats and their times, we calculate the common speed. The boats travel at a speed of 0.5 miles per minute.
Step-by-step explanation:
We're given that two boats travel at the same speed to different destinations. One key is to realize that speed is distance divided by time. If Boat A reaches its destination in 12 minutes and Boat B in 18 minutes and Boat B travels 3 miles farther than Boat A, we can set up an equation to solve for the common speed of both boats.
Let's denote the speed of the boats as s in miles per minute. We don't know the distance Boat A traveled so let's call it d. Then Boat B traveled d + 3 miles.
For Boat A: The total distance is speed times time, or s × 12 minutes = d miles.
For Boat B: Using the same formula gives us s × 18 minutes = d + 3 miles.
To find the speed s, we can set up two equations:
- s × 12 = d
- s × 18 = d + 3
From equation 1, d = 12s.
Plug d into equation 2:
18s = 12s + 3
6s = 3
s = 3 / 6 = 0.5 miles per minute
Therefore, the boats travel at 0.5 miles per minute.