There is a lighthouse that is 4 miles from the closest point, B, on a straight beach. 4 miles east of B, is point C. If the keeper of the lighthouse can row his boat at 3 mi/h and walk at 5 mi/h (On a treadmill, I speedwalk at approximately 4.6 mi/h, so this guy must be pretty fit!). Find the distance between B and C he should land to minimize time taken.

For this, I let x be the distance between B and D, the point where he would land his boat.

The distance traveled across water would then be

Wouldn't the equation be

thus,

So, I was wondering if this was just a faulty problem, if I messed up, or what. I feel like I overlooked something ridiculous.