A runner and a walker begin on a track (oval shape) 1 mile in length at the same spot and depart in opposite directions. The runner goes steadily at 9 mph while the walker goes at a steady 3 mph. How long before they meet again? Show your work!
Let the distance covered by the slower walker be x, then clearly the distance covered by the faster walker would be 1-x.
Now the time taken by the slower walker is x/3 and the time taken by the faster walker would be ......??
What do you know about the times taken by each??
Can you take it from here?
hint: 1/12 hour which would be 5 minutes.
Let the distance covered by the slower walker be x, then clearly the distance covered by the faster walker would be 1-x.
Now the time taken by the slower walker is x/3 and the time taken by the faster walker would be ......??
What do you know about the times taken by each??
Can you take it from here?
hint: 1/12 hour which would be 5 minutes.
To find the time taken by the faster runner, we need to use the formula:
time = distance / speed
For the slower walker, the time taken is x/3 (since the speed is 3 mph and the distance covered is x).
For the faster runner, the time taken is (1-x)/9 (since the speed is 9 mph and the distance covered is 1-x).
Since they both begin at the same spot and depart in opposite directions, the total time taken by both of them would be the same.
So, x/3 = (1-x)/9
To solve for x, we can cross multiply:
9x = 3(1-x)
9x = 3 - 3x
12x = 3
x = 3/12
x = 1/4
This means the slower walker covers 1/4 of a mile before they meet again.
Now, we need to find the time it takes for the runners to meet. We can use the formula:
time = distance / speed
For the slower walker, the time taken is (1/4) / 3 = 1/12 hour.
Since 1 hour is equal to 60 minutes, the time taken is (1/12) * 60 = 5 minutes.
Therefore, the runner and the walker will meet again after 5 minutes.