Andy and Kate are running around a 400-meter track. If they run in the same direction, Andy will pass Kate in 100 seconds. If they run in the opposite direction, they will meet in 25 seconds. What is Andy's velocity in meters per second?
4
6
10
16
Explain your answer.
I have to assume that they start in the same place, running in opposite directions. Running in the same direction, you get the time for Andy to "lap" Kate:
Va*100 - Vk*100 = 400 meters
which means
Va - Vk = 4 m/s
Running in opposite directions, they start out 400 meters (one track length)apart (although in the same place), and close the distance at a rate Va + Vk
(Va+ Vk)*25 = 400
Va + Vk = 16 m/s
2 Va = 20
Va = 10 m/s is Andy's speed.
(He would be a world record holder at that speed; the record is about 9.3 m/s for 400 m)
Vk = 6 m/s
There is something wrong either with the problem or with the answer. The answer must be only one number. It cannot be 4 miles per second AND 6 miles per second.
Explain, please.
The answer you want is Va (Andy's velocity), 10 m/s. I was just trying to show you more of the steps of solving the problem. I never said the answer was 4 m/s. That is the DIFFRERENCE between the speeds. You did not read my answer very carefully. If you had, you would have found:
<<Va = 10 m/s is Andy's speed. >>
Thank you for clarifying. You are dealing with a dense old lady this morning.
M.A. , drwls did not say they went 4 miles per second AND 6 miles per second
The velocity is in m/s , which is metres per second.
The conclusion was that Andy's velocity was 10 m/s
and Kate's velocity was 6 m/s
I agree with drwls about Andy's speed.
At his speed he would be with the world's elite runners.
http://en.wikipedia.org/wiki/100_metres#Record_performances
I perhaps should have said my speeds were meters per second. Since it was a 400 meter track and "m" is the standard abbreviation for meters, I figured that was obvious.
Although some elite runners have averaged faster than 10 m/s for 100 and 200 meters, nobody has done it for 400 meters. The human body cannot sustain maximum speeds for more than about 250 m, even for the very best runners. It has something to do with anaerobic threshholds.
To solve this problem, we need to understand the concept of relative velocity.
When Andy and Kate are running in the same direction, their velocities add up. In this case, Andy will pass Kate in 100 seconds. We can set up the equation:
Andy's velocity - Kate's velocity = Distance/Time
Let's assume Andy's velocity is 'v' and Kate's velocity is 'k'. The distance they cover in 100 seconds is 400 meters (the length of the track).
So, the equation becomes:
v - k = 400/100
Simplifying the equation, we get,
v - k = 4
Now, when Andy and Kate are running in opposite directions, their velocities subtract. In this case, they will meet in 25 seconds.
The equation becomes:
v + k = 400/25
Simplifying the equation, we get,
v + k = 16
Now, we have a system of equations:
v - k = 4
v + k = 16
We can solve this system of equations using any method, such as substitution or elimination. Subtracting the two equations, we get:
2v = 20
v = 10
Therefore, Andy's velocity is 10 meters per second.
So, the correct answer is 10.