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?
To find the answer, we first need to calculate the time it takes for both Pamela and Josalin to run 400 meters. We can then compare the time difference to determine how far ahead Pamela would be when crossing the finish line.
First, let's calculate Pamela's time to run 400 meters. We can set up a proportion using the given information:
100 meters / 12.5 seconds = 400 meters / x seconds
To find x, we can cross-multiply and solve for it:
100 * x = 12.5 * 400
x = (12.5 * 400) / 100
x = 50
Therefore, Pamela would take 50 seconds to run 400 meters.
Now, let's calculate Josalin's time to run 400 meters using the same method:
150 meters / 20 seconds = 400 meters / y seconds
Cross-multiplying and solving for y:
150 * y = 20 * 400
y = (20 * 400) / 150
y = 53.33 (rounded to two decimal places)
Therefore, Josalin would take approximately 53.33 seconds to run 400 meters.
Now, let's find the time difference between Pamela and Josalin:
Time difference = Pamela's time - Josalin's time
Time difference = 50 seconds - 53.33 seconds
Time difference = -3.33 seconds
Since the time difference is negative, it means Pamela crossed the finish line after Josalin. Therefore, Pamela would not be ahead of Josalin when crossing the finish line in a 400 meter race.
To find out how many meters ahead Pamela would cross the finish line before Josalin, we need to compare their speeds.
To find Pamela's speed, we divide the distance she can run by the time it takes her:
Pamela's speed = 100 meters ÷ 12.5 seconds = 8 meters per second
To find Josalin's speed, we divide the distance she can run by the time it takes her:
Josalin's speed = 150 meters ÷ 20 seconds = 7.5 meters per second
Now, let's calculate the time it would take Pamela to run 400 meters:
Pamela's time to run 400 meters = 400 meters ÷ 8 meters per second = 50 seconds
Similarly, let's calculate the time it would take Josalin to run 400 meters:
Josalin's time to run 400 meters = 400 meters ÷ 7.5 meters per second = 53.33 seconds (rounded to 2 decimal places)
To find out how many meters ahead Pamela would be, we subtract the time it takes Josalin from the time it takes Pamela and multiply the difference by Pamela's speed:
Difference in time = 50 seconds - 53.33 seconds = -3.33 seconds (rounded to 2 decimal places)
Meters ahead = -3.33 seconds x 8 meters per second = -26.64 meters (rounded to 2 decimal places)
Since a negative value indicates that Josalin would finish before Pamela, we can say that Josalin would cross the finish line approximately 26.64 meters ahead of Pamela.