211k views
5 votes
the current of a river is 2 miles per hour. a boat travels to a point 24 miles up stream and back in 5 hours . what is the speed of the boat in still water​

1 Answer

4 votes

Let's denote the speed of the boat in still water as "b", and let's denote the distance between the two points as "d" (in this case, d = 24 miles).

When the boat is traveling upstream against the current, its effective speed is b - 2 mph (since the current is working against the boat). When the boat is traveling downstream with the current, its effective speed is b + 2 mph (since the current is helping the boat).

We know that the boat travels a total distance of 24 miles upstream and then 24 miles downstream, for a total distance of 48 miles. We also know that the total time it takes for the boat to make this round trip is 5 hours. So we can set up the following equation:

24/(b-2) + 24/(b+2) = 5

Multiplying both sides by (b-2)(b+2), we get:

24(b+2) + 24(b-2) = 5(b-2)(b+2)

Simplifying and rearranging, we get:

10b^2 - 96b - 208 = 0

We can solve this quadratic equation using the quadratic formula:

b = (-(-96) ± sqrt((-96)^2 - 4(10)(-208))) / (2(10))

b = (96 ± sqrt(96^2 + 8320)) / 20

b = (96 ± sqrt(9024)) / 20

b = (96 ± 96) / 20

So the possible values of b are b = 9.6 or b = -0.8. We can discard the negative value since it doesn't make sense as a speed, so we have:

b = 9.6 mph

Therefore, the speed of the boat in still water is 9.6 miles per hour

User Peter Jacobs
by
8.0k points

No related questions found