Let's start by setting up some equations to represent the given information.
Let Luis's speed be x miles per hour.
Then Manuel's speed is 3x miles per hour.
We know that it takes Luis 4 hours longer than Manuel to travel 96 miles. Let's use the formula:
time = distance / speed
For Luis:
96 / x = t + 4
For Manuel:
96 / (3x) = t
where t is the time in hours for each person to travel 96 miles.
We want to solve for Luis's speed x, so let's eliminate t by setting the two expressions equal to each other and solving for x:
96 / x = 96 / (3x) + 4
Multiplying both sides by 3x, we get:
288 = 96 + 12x
Subtracting 96 from both sides, we get:
192 = 12x
Dividing both sides by 12, we get:
x = 16
So Luis can ride his bicycle at a speed of 16 miles per hour.