Mike can run the mile in 6 minutes, and Dan Can run the mile in 9 minutes. If mike gives Dan a head start of 1 minute, how far from the start will mike pass Dan? How long does it take?
They run the same distance.
Mikedistance=1mile/6min * (time-1)
Dandistance=1mile/9min * time
set the two distance equal
1mile/6min (time-1)=1mile/9min (time
or
9(time-1)=6time
you do it from here.
time will be in minutes.
How far? use either distance equation.
To find out how far from the start Mike will pass Dan, we need to first calculate how far each person can run in the given time intervals.
Since Mike can run the mile in 6 minutes, his running speed is 1 mile / 6 minutes, which is equivalent to 1/6 miles per minute. Similarly, Dan's running speed is 1 mile / 9 minutes, or 1/9 miles per minute.
If Mike gives Dan a head start of 1 minute, Dan will have already run for 1/9 miles (his speed) in that time. Therefore, Mike needs to catch up by running this distance plus an extra distance to pass Dan.
To calculate the extra distance Mike needs to run to pass Dan, we can use the equation: Extra Distance = Mike's Speed × Time.
Mike's speed is 1/6 miles per minute, and the time it takes to catch up to Dan is 1 minute. Substituting these values into the equation, we get:
Extra Distance = (1/6) miles/minute × 1 minute = 1/6 mile.
Therefore, Mike needs to run an extra 1/6 mile to pass Dan.
To determine how long it takes for Mike to pass Dan, we simply need to add the 1 minute head start that Dan had to the extra time it takes for Mike to run the extra distance.
The time it takes for Mike to run the extra distance can be calculated using the equation: Time = Distance / Speed.
The distance Mike needs to run to pass Dan is 1/6 mile, and Mike's running speed is 1/6 miles per minute. Substituting these values into the equation, we get:
Time = (1/6) mile / (1/6) miles/minute = 1 minute.
Therefore, it takes an additional 1 minute for Mike to run the extra distance and pass Dan. Adding this to the 1 minute head start that Dan had, we get a total time of:
Total Time = 1 minute (head start) + 1 minute (extra time) = 2 minutes.
So, Mike will pass Dan at a distance of 1/6 mile from the start, and it will take him a total of 2 minutes to do so.