Leah takes 1.5 hours to catch up with Raul.
Step-by-step explanation:
To determine how long it takes Leah to catch up with Raul, we can use the formula:
Distance = Rate × Time
Let's assume the time it takes Leah to catch up with Raul is 't' hours.
Raul bikes a distance of 6 miles at a rate of 3 miles per hour, so his time is:
Time = Distance / Rate = 6 miles / 3 miles per hour = 2 hours.
Leah starts biking 30 minutes (or half an hour) later than Raul. So when Leah starts, Raul has already been biking for 2 hours. Since Leah's rate is 4 miles per hour, her distance covered in 't' hours is:
Distance = Rate × Time = 4 miles per hour × t hours.
Since Raul and Leah cover the same distance, we can equate the distances:
2 hours × 3 miles per hour = 4 miles per hour × t hours.
Simplifying this equation gives us:
6 miles = 4t miles.
Dividing both sides of the equation by 4 gives:
t = 6 / 4 = 1.5 hours.
Therefore, it takes Leah 1.5 hours to catch up with Raul.