7. 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.

Here's how to solve this problem:<br /><br />**1. Define Variables:**<br /><br />* Let 'r' be Tyler's rowing speed in still water (km/h).<br />* Let 'c' be the speed of the current (km/h).<br /><br />**2. Set up Equations:**<br /><br />* **Downstream:** When rowing downstream, the current *adds* to Tyler's speed. The distance is 10 km and the time is 2 hours. So, the equation is: r + c = 10/2 or r + c = 5<br /><br />* **Upstream:** When rowing upstream, the current *subtracts* from Tyler's speed. The distance is 8 km and the time is 4 hours. So, the equation is: r - c = 8/4 or r - c = 2<br /><br />**3. Solve the System of Equations:**<br /><br />We have two equations with two unknowns:<br /><br />* r + c = 5<br />* r - c = 2<br /><br />The easiest way to solve this is using elimination. Add the two equations together:<br /><br />(r + c) + (r - c) = 5 + 2<br /><br />This simplifies to:<br /><br />2r = 7<br /><br />Therefore:<br /><br />r = 7/2 = 3.5 km/h<br /><br />Now substitute this value of 'r' back into either of the original equations. Let's use the first one:<br /><br />3.5 + c = 5<br /><br />c = 5 - 3.5<br /><br />c = 1.5 km/h<br /><br />**4. Determine Average Rowing Speed:**<br /><br />Tyler's average rowing speed is his speed in still water, which we calculated as 3.5 km/h.<br /><br />**Answer:**<br /><br />Tyler's average rowing speed is 3.5 km/h, and the speed of the current is 1.5 km/h.<br />