Question

A motorboat can maintain a constant speed of 11 miles

per hour relative to the water. The boat makes a trip
upstream to a certain point in 26 minutes; the return trip
takes 18 minutes. What is the speed of the current?
The speed of the current is
mile(s) per hour.

Answer 1

2 miles per hour.

Explanation:

When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the current. Therefore, the boat's speed relative to the ground (or still water) during the upstream trip is 11 - c miles per hour.

Similarly, when the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. Therefore, the boat's speed relative to the ground during the downstream trip is 11 + c miles per hour.

Given that the boat takes 26 minutes (or 26/60 hours) to make the upstream trip and 18 minutes (or 18/60 hours) to make the downstream trip, we can set up the following equations:

Distance = Speed × Time

For the upstream trip:

Distance = (11 - c) × (26/60)

For the downstream trip:

Distance = (11 + c) × (18/60)

Since the distances traveled in both directions are the same (as the boat goes to the same point and returns), we can equate the two equations:

(11 - c) × (26/60) = (11 + c) × (18/60)

Let's solve this equation to find the value of "c" (the speed of the current):

(11 - c) × (26/60) = (11 + c) × (18/60)

(11 - c) × 26 = (11 + c) × 18

286 - 26c = 198 + 18c

44c = 88

c = 88/44

c = 2