A runner and a walker depart from the same point going in opposite directions on a circular track that is 1 mile long. The runner travels at 9 mph and the walker at 3 mph. After how many minutes will they pass each other?
I know the answer is 5 but I don't know how to get it
let the time passed be t hrs
When they meet, let the faster have gone x miles
then the slower has gone 1-x miles
time of faster = x/9
time of slower = (1-x)/3
but, when they meet, each has gone the same time, so
x/9 = (1-x)/3
3x = 9 - 9x
12x = 9
x = 9/12
time of faster = (9/12) รท 9
= 1/12 hrs
or 5 minutes
or, consider that the walker covers 1/4 mile while the runner covers 3/4 mile.
(1/4 mi)/(3 mi/hr) = 1/12 hr = 5 min.
To determine how many minutes it will take for the runner and the walker to pass each other, we need to consider their relative speeds.
Since they are moving in opposite directions, we can add their speeds together to find the total relative speed: 9 mph + 3 mph = 12 mph.
Now, we can convert this relative speed from miles per hour to miles per minute, since we want to find the time in minutes. There are 60 minutes in an hour, so we divide the relative speed by 60: 12 mph / 60 = 0.2 miles per minute.
Since the circular track is 1 mile long, the runner and the walker will meet each other once they collectively travel a distance of 1 mile. To find the time it takes to cover this distance, we divide the distance by the relative speed: 1 mile / 0.2 miles per minute = 5 minutes.
Therefore, it will take 5 minutes for the runner and the walker to pass each other on the circular track.