Q37: First, we have to figure out how far the hiker is from the biker after 5 minutes. Since they're both traveling in the same direction, you can subtract the smaller rate from the bigger rate to get the overall rate.
So, the biker and the hiker were getting further away from each other at the rate of 20-4 = 16 mile per hour, or 16 mile per 60 minutes. After 5 minutes, they will be:
(16 miles / 60 minutes) x 5 minutes = 4/3 miles apart.
The question asks how long the biker have to wait for the hiker to catch up with him.
(4/3 miles) x (60 minutes / 4 miles) = 20 minutes.
For the other question- I think that when you have a triangle whose two legs are of constant length, the triangle's area is maximized when the 2 legs come together at 90 degree.
In this case, we know that the length of each legs are 1 because that's the radius of the circle (given).
