Question

Manuel can drive 3 times as fast as Luis can ride his bicycle.

If it takes Luis 4 hours longer than Manuel to travel 96
miles, how fast can Luis ride his bicycle?

Answer 1

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.