Brandon is on one side of a river that is 60 m
wide and wants to reach a point 200m downstream on the opposite side as quickly as possible by swimming diagonally across the river and then running the rest of the way. Find the minimum amount of time if Brandon can swim at
2m/s and run at 4m/s. I keep getting 65.83 and that is not the correct answer what am I doing wrong?
To find the minimum amount of time for Brandon to reach the point on the opposite side, we can break down the problem into two parts: swimming across the river and running to the destination.
Let's calculate the time it takes to swim across the river first. We can use the Pythagorean theorem to find the distance Brandon needs to swim diagonally:
diagonal distance = √(width of the river)^2 + (distance downstream)^2
= √(60m)^2 + (200m)^2
≈ 208.206m
Now, we can calculate the time it takes for Brandon to swim across the river:
time to swim = distance / speed
= 208.206m / 2m/s
≈ 104.103 seconds
Next, we need to calculate the time it takes for Brandon to run the remaining distance:
distance remaining = width of the river
= 60m
time to run = distance remaining / speed
= 60m / 4m/s
= 15 seconds
Finally, we can find the total time by adding the time to swim and the time to run:
total time = time to swim + time to run
≈ 104.103 seconds + 15 seconds
≈ 119.103 seconds
Therefore, the minimum amount of time for Brandon to reach the point on the opposite side is approximately 119.103 seconds.