Pedro and Ivan raced each other in a 24-mile bike race. After 2o minutes, Pedro traveled 5 miles. Ivan had spent the 20 minutes travelling at a rate of 16 miles per hour. Which person was in first place after 20 minutes? Use words and/or numbers to show how you determined your answer?
20 minutes is 1/3 hour
So, Ivan had gone 16/3 = 5 1/3 miles
To determine which person was in first place after 20 minutes, we need to compare the distances traveled by Pedro and Ivan.
Given that Pedro traveled 5 miles in 20 minutes, we can calculate his speed as follows:
Speed = Distance / Time = 5 miles / 20 minutes
Since we want the speed in miles per hour, we need to convert the time to hours:
20 minutes = 20/60 = 1/3 hour
So Pedro's speed is: 5 miles / (1/3 hour) = 5 miles * (3/1) = 15 miles per hour.
Now let's calculate the distance Ivan traveled in 20 minutes if his speed is 16 miles per hour:
Speed = Distance / Time
16 miles per hour = Distance / (20 minutes)
Again, we need to convert the time to hours:
20 minutes = 20/60 = 1/3 hour
So the distance Ivan traveled in 20 minutes is: 16 miles per hour * (1/3 hour) = 16 miles * (1/3) = 16/3 miles.
Comparing the distances traveled, we find that Pedro traveled 5 miles and Ivan traveled approximately 5.33 miles (16/3 miles). Therefore, after 20 minutes, Ivan was in the lead because he covered a greater distance.