One competitor in a 100-mile bicycle race took a total of 5 hours to complete the

Let x = morning ride time, y = afternoon ride time.

We set up two different equations to represent the given info in the description. The first one is morning time + afternoon time = total time to complete the course. So it's x + y = 5. Next, we do morning average multiplied by morning ride time + afternoon average multiplied by afternoon ride time = total distance. So it's 23x + 13y = 100. Then, set up a system of equations:

x + y = 5
23x + 13y = 100

Now, we must pick which variable we want to solve for first. This way we can plug the number we solve for back into one of the original equations to find the other missing variable. I'm going to solve for x first so we multiply by the first equation by - 13. You'll see why in a bit. 

- 13(x + y = 5) >> - 13x - 13y = - 65

Your new system of equations is:

- 13x - 13y = - 65
23x + 13y = 100

Now we combine like terms amongst the two equations. Notice the y-variables will cancel each other out, leaving us with just the x to solve for like I want. 

10x = 35

Divide by 10 on both sides to isolate variable x

x = 35/10 or 3.5

Now that we have x, we solve for y. Plug your x-value back into either equation; I choose the first because it's easiest. 

3.5 + y = 5

Subtract 3.5 from both sides to isolate variable y.

3.5 + y - 3.5 = 5 - 3.5
y + 0 = 1.5
y = 1.5

So the competitor rode 3.5 hours in the morning and 1.5 hours in the afternoon. 

OR

The competitor rode 3 hours, 30 minutes in the morning and 1 hour, 30 minutes in the afternoon. 

49.92 miles/hour

Step-by-step explanation:

32 miles/hour = 32 * 5280 = 168960 ft/hour

For the collision to occur, both cars must arrive at the intersection at the same time.

The time it takes for the Mercedes to travel 400 feet at the rate of 168960 ft/hour is 400 / 168960 = 0.002367 hours

So the Ferrari should take the same time to travel 624 feet as well, its speed would be

624 / 0.002367 = 263577.6 ft/hour or 263577.6 / 5280 = 49.92 miles/hour