Joel can run around a 1/4 mi track in 66 sec. Jason can run around the track in 60 sec.If the runners start at the same point on the track and run in opposite directions, how long will it take the runners to cover 1/4 mile?
let the time it took be t seconds
they ran the same time
speed of faster runner = .25/60 mi/s =1/240 mi/s
speed of slower runner = .25/66 mi/s = 1/264 mi/s
(1/240)t + (1/264)t = 1/4
(7/880)t = 1/4
t = (1/4)(880/7) = 220/7 seconds
or appr 31.43 seconds
To find out how long it will take the runners to cover 1/4 mile when running in opposite directions, we can add their individual times.
Joel takes 66 seconds to run around the track once.
Jason takes 60 seconds to run around the track once.
Since they are running in opposite directions, they will meet each other after covering a distance equal to the sum of their distances.
So, the total distance they need to cover together is 1/4 + 1/4 = 1/2 mile.
Now, we can calculate the time it will take for them to cover 1/2 mile.
Joel takes 66 seconds to run 1/4 mile. Therefore, it will take him 66 * 2 = 132 seconds to run 1/2 mile.
Jason takes 60 seconds to run 1/4 mile. Therefore, it will take him 60 * 2 = 120 seconds to run 1/2 mile.
Therefore, it will take the runners 132 seconds and 120 seconds, respectively, to cover 1/2 mile together.
To find out how long it will take the runners to cover 1/4 mile when they start at the same point and run in opposite directions, we need to determine how much distance each runner covers in one second.
First, let's find out how much distance Joel covers in one second. We know that Joel can run around a 1/4 mile track in 66 seconds. Therefore, we can calculate his speed as follows:
Joel's speed = Distance / Time = 1/4 mile / 66 seconds = 1/264 mile per second.
Similarly, we can find out how much distance Jason covers in one second. We know that Jason can run around the same track in 60 seconds. So his speed would be:
Jason's speed = Distance / Time = 1/4 mile / 60 seconds = 1/240 mile per second.
Since the runners are running in opposite directions, their speeds add up. So, to find out how long it will take for them to cover 1/4 mile, we can add their speeds together:
Total speed = Joel's speed + Jason's speed
= 1/264 mile per second + 1/240 mile per second.
To add these fractions, we need to find a common denominator. In this case, the least common denominator (LCD) is 5280.
Now, we can rewrite the fractions using the LCD:
Total speed = (1/264) / (1/5280) mile per second + (1/240) / (1/5280) mile per second.
Simplifying these fractions:
Total speed = 20/5280 + 22/5280 mile per second
= 42/5280 mile per second
= 1/125 mile per second.
Since speed is defined as distance divided by time, we can rearrange the equation to find the time it takes to cover a certain distance:
Time = Distance / Speed.
For this problem, we want to find the time it takes to cover 1/4 mile, so we can plug in the values:
Time = 1/4 mile / (1/125 mile per second).
Simplifying this expression:
Time = 1/4 * 125 seconds
= 125/4 seconds
= 31.25 seconds.
Therefore, it will take the runners approximately 31.25 seconds to cover 1/4 mile when they start at the same point and run in opposite directions.
or, consider this a normal work problem:
1/60 + 1/66 = 1/t
t = 220/7