Pamela can run 100 meters in 12.5 seconds and Josalin can run 150 meters in 20 seconds. If they both ran a 400 meter race at this rate, how many meters ahead would Pamela cross the finish line before Josalin?
time = distance/speed, so
(400/(150/20)-400/(100/12.5))(100/12.5) = 26.66m
To find out how many meters ahead Pamela would cross the finish line before Josalin in a 400-meter race, we need to determine the time it takes for each of them to run 400 meters.
First, let's calculate the time it takes Pamela to run 400 meters. Since she can run 100 meters in 12.5 seconds, we can set up a proportion:
100 meters / 12.5 seconds = 400 meters / x seconds
To find x (the time it takes Pamela to run 400 meters), we can cross-multiply:
100 meters * x seconds = 12.5 seconds * 400 meters
Simplifying this equation, we get:
100x = 12.5 * 400
100x = 5000
Now, divide both sides of the equation by 100 to solve for x:
x = 5000 / 100
x = 50
Therefore, Pamela can run 400 meters in 50 seconds.
Next, let's calculate the time it takes Josalin to run 400 meters. Since Josalin can run 150 meters in 20 seconds, we can also set up a proportion:
150 meters / 20 seconds = 400 meters / y seconds
To find y (the time it takes Josalin to run 400 meters), we can cross-multiply:
150 meters * y seconds = 20 seconds * 400 meters
Simplifying this equation, we get:
150y = 20 * 400
150y = 8000
Now, divide both sides of the equation by 150 to solve for y:
y = 8000 / 150
y = 53.33 (rounded to two decimal places)
Therefore, Josalin can run 400 meters in approximately 53.33 seconds.
Since Pamela takes 50 seconds to run 400 meters and Josalin takes 53.33 seconds to run the same distance, we can subtract the time it takes Josalin from the time it takes Pamela:
50 seconds - 53.33 seconds = -3.33 seconds
Since Pamela finishes 3.33 seconds ahead of Josalin, we need to figure out how far Pamela would have run in that time.
To find the distance Pamela runs in 3.33 seconds, we'll use the rate at which she runs 400 meters.
The distance Pamela would run in 1 second is 400 meters divided by 50 seconds:
400 meters / 50 seconds = 8 meters per second
Now, we multiply Pamela's rate by the time difference:
8 meters/second * 3.33 seconds = 26.64 meters
Therefore, Pamela would cross the finish line 26.64 meters ahead of Josalin.