Question

Tyler rows 10 km downstream in 2 h. On the return trip, it takes him 4 h to travel 8 km. Determine his average rowing speed and the speed of the current.

Answer 1

Tyler's average rowing speed in still water is 3.5 km/h, while the speed of the current is 1.5 km/h, calculated by solving a system of equations derived from his downstream and upstream trip times and distances.

Step-by-step explanation:

To determine Tyler's average rowing speed and the speed of the current, we need to consider both the downstream and upstream motions separately.

Let u be the rowing speed of the boat in still water and v be the speed of the current. When Tyler rows downstream, the effective speed of the boat is (u + v), and when he rows upstream, it is (u - v).

For the downstream trip, we use the formula speed = distance/time to find that:

u + v = 10 km / 2 h = 5 km/h

For the return upstream trip, we again use the formula:

u - v = 8 km / 4 h = 2 km/h

We can set up a system of equations to solve for u and v:

1. u + v = 5 km/h
2. u - v = 2 km/h

Solving these equations, we find:

• u = (5 km/h + 2 km/h) / 2 = 3.5 km/h
• v = (5 km/h - 2 km/h) / 2 = 1.5 km/h

Tyler's average rowing speed in still water is 3.5 km/h, and the speed of the current is 1.5 km/h.