Question

Alex is motorboat took four hours to make a trip down stream with a 5 mph current. The return trip against the same current took six hours. Find the speed of the boat in Stillwater and the distance he traveled.

Answer 1

To find the speed of the boat in still water and the distance traveled, we can use the concept of relative velocity.

Step-by-step explanation:

To find the speed of the boat in still water and the distance traveled, we can use the concept of relative velocity.

Let x be the speed of the boat in still water, and let d be the distance traveled.

For the downstream trip, the boat is moving with the current, so the effective speed of the boat is x + 5 mph. And since the time taken is 4 hours, we have the equation: d = (x + 5) * 4.

For the return trip against the current, the effective speed of the boat is x - 5 mph, and the time taken is 6 hours. So we have the equation: d = (x - 5) * 6.

By solving these two equations simultaneously, we can find the values of x and d.

Answer 2

25 mph

120 miles

Step-by-step explanation:

We have that the speed is equal to:

v = d / t

if we solve for distance:

d = v * t

in this case, since it is the same route both outward and back, the distances are equal, therefore:

v1 * t1 = v2 * t2

t1 = 4 hours

t2 = 6 hours

v1 = x + 5 (downstream speed)

v2 = x -5 (upstream speed)

replacing:

(x + 5) * 4 = (x - 5) * 6

4 * x + 20 = 6 * x - 30

6 * x - 4 * x = 20 + 30

2 * x = 50

x = 25

speed is 25 mph

now the distance would be:

d = (25 + 5) * 4 = 120

d = (25 - 5) * 6 = 120

In other words, the route was 120 miles.