Question

A remote-controlled boat traveled 14 feet heading east and 54 feet heading north, totaling 68 feet over the course of 16 seconds. Heading east, the boat traveled at an average speed 4 feet per second less than its speed heading north. What was the average speed of the boat heading north? (Do not include the units in your response.)

Answer 1

The average speed of the boat heading north is 4 feet per second.

Step-by-step explanation:

To find the average speed of the boat heading north, we need to first find the time it took for the boat to travel each distance. We can find the time by dividing the distance traveled by the speed. Let's denote the speed heading north as S and the speed heading east as S - 4.

For the distance traveled heading east, we have:

14 feet = (S - 4) feet/second * time

For the distance traveled heading north, we have:

54 feet = S feet/second * time

Since the total distance is 68 feet and the total time is 16 seconds, we can write:

14 feet + 54 feet = (S - 4) feet/second * time + S feet/second * time

68 feet = S*time + S*time - 4*time

68 feet = 2S*time - 4*time

68 feet = (2S - 4)*time

68/((2S - 4)) = time

Now, we can substitute the value of time into the equation for the distance traveled heading north to find the speed:

54 feet = S feet/second * (68/((2S - 4)))

Solving for S, we get:

S = 4 feet/second