In a marathon race Chad is out in front, running due north at a speed of 3.87 m/s. John is 98 m behind him, running due north at a speed of 4.63 m/s. How long does it take for John to pass Chad?
Why did John run faster than Chad in the marathon? He must have really stepped up his game! To find out how long it takes for John to pass Chad, we need to determine the time it takes for John to cover the 98-meter distance between them.
Let's first convert their speeds into meters per minute. Chad is running at 3.87 m/s, which is 232.2 m/min (approximately). John is running at 4.63 m/s, which is 277.8 m/min (approximations are fun!).
Now, we can calculate the time it takes for John to cover the 98-meter distance. Since distance equals speed multiplied by time, we can use the formula time = distance / speed.
For John: time = 98 m / 277.8 m/min = 0.352 minutes (approximately).
So, John will catch up to Chad in just about 0.352 minutes, or approximately 21 seconds. By then, Chad better have made way for John, or else he might be tripped up by more than just John's speed!
To find the time it takes for John to pass Chad, we need to determine the relative speed between them.
The relative speed is the difference in their speeds: 4.63 m/s - 3.87 m/s = 0.76 m/s.
Next, we can calculate the time it takes for John to cover the remaining distance of 98 m, using the relative speed of 0.76 m/s.
Time = Distance / Speed
Time = 98 m / 0.76 m/s ≈ 128.95 s
Therefore, it takes approximately 128.95 seconds for John to pass Chad.
To find out how long it takes for John to pass Chad, we need to determine the distance between them and compare their speeds.
Let's assume that the time it takes for John to pass Chad is t seconds.
In that time, Chad will have run a distance of:
Distance_Chad = Speed_Chad * t
John will have run a distance of:
Distance_John = Speed_John * t
The distance between them can be calculated by subtracting Chad's distance from John's distance:
Distance_Difference = Distance_John - Distance_Chad
As given in the question, Chad is initially 98 m ahead of John. So, the equation becomes:
Distance_Difference = Distance_John - Distance_Chad
Distance_Difference = Distance_John - (Distance_Chad + 98)
Now, let's substitute the distance formula we calculated earlier into the equation:
Distance_Difference = (Speed_John * t) - (Speed_Chad * t) - 98
Simplifying further:
Distance_Difference = (4.63 * t) - (3.87 * t) - 98
Distance_Difference = (0.76 * t) - 98
To find the time t when John passes Chad, we set the Distance_Difference to zero since they will be at the same position:
0 = (0.76 * t) - 98
Now, let's solve for t:
0.76 * t = 98
t = 98 / 0.76
Using a calculator, t ≈ 128.95 seconds.
Therefore, it takes approximately 128.95 seconds for John to pass Chad in the race.