A boat travels down the river in 2.3 hours. The return trip up river takes 3.7 hours. A one way trip down or up river is a distance of 26 miles. If the boat is traveling at maximum speed, what is the boats speed measured in waters with no current? You need to use systems to solve this problem. Round your speed to the tenth of a mile per hour.

Question

A boat travels down the river in 2.3 hours. The return trip up river takes 3.7 hours. A one way trip down or up river is a distance of 26 miles. If the boat is traveling at maximum speed, what is the boats speed measured in waters with no current? You need to use systems to solve this problem. Round your speed to the tenth of a mile per hour.

Answer 1

if the boat has speed b and the river has speed r,

2.3(b+r) = 26
3.7(b-r) = 26

b=9.2
r=2.1

Answer 2

which one would represent the water with no current?

Answer 3

come on. the water has a current. I said b was the speed of the boat.

Answer 4

To solve this problem using systems, we need to set up equations representing the boat's speed and the current.

Let's assume the boat's speed measured in still waters is "b" miles per hour, and the speed of the river's current is "c" miles per hour. We want to find "b".

For the trip down the river, the boat's effective speed will be the sum of its speed in still waters and the speed of the current: "b + c".

Similarly, for the return trip up the river, the boat's effective speed will be the difference between its speed in still waters and the speed of the current: "b - c".

The time taken for each trip can be used to set up the equations:

For the trip down the river:
Time = Distance / Speed
2.3 = 26 / (b + c) -------- (Equation 1)

For the return trip up the river:
Time = Distance / Speed
3.7 = 26 / (b - c) -------- (Equation 2)

Now, solve this system of equations to find the values of "b" and "c".

Start by rearranging Equation 1 to solve for (b + c):
(b + c) = 26 / 2.3

Simplify the right side:
(b + c) = 11.3

Next, rearrange Equation 2 to solve for (b - c):
(b - c) = 26 / 3.7

Simplify the right side:
(b - c) = 7.03

Now, we have a system of equations:
(b + c) = 11.3 -------- (Equation 3)
(b - c) = 7.03 -------- (Equation 4)

We can solve this system by adding Equation 3 and Equation 4:

(b + c) + (b - c) = 11.3 + 7.03

Simplify:
2b = 18.33

Divide both sides by 2:
b = 9.165

So, the boat's speed measured in still waters, rounded to the nearest tenth of a mile per hour, is approximately 9.2 miles per hour.