A motorboat can maintain a constant speed of 26 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 35 minutes; the return trip takes 17 minutes. What is the speed of the river current?

To find the speed of the river current, we need to set up and solve an equation using the given information.

Let's assume that the speed of the river current is "r" miles per hour.

For the trip upstream, the boat is traveling against the current. Therefore, the effective speed of the boat is reduced by the speed of the river current. So, the speed of the boat relative to the ground is (26 - r) mph.

We know that the time it takes for the upstream trip is 35 minutes, or 35/60 = 7/12 hours.

Using the formula: Speed = Distance / Time, we can set up the equation for the upstream trip:

(26 - r) mph = Distance / (7/12) hours

Simplifying, we have: Distance = (26 - r) * (7/12)

Now, let's consider the return trip, where the boat is traveling with the current. In this case, the effective speed of the boat is increased by the speed of the river current. So, the speed of the boat relative to the ground is (26 + r) mph.

The time it takes for the return trip is given as 17 minutes, or 17/60 = 17/60 hours.

Using the same formula, we can set up the equation for the return trip:

(26 + r) mph = Distance / (17/60) hours

Simplifying, we have: Distance = (26 + r) * (17/60)

Since the distance traveled for the upstream and return trips is the same, we can set the two expressions for distance equal to each other:

(26 - r) * (7/12) = (26 + r) * (17/60)

Now, we can solve this equation for "r", the speed of the river current.