azmin decided to get some exercise by taking the stairs from the first to the fifth floor in her apartment building. The first time she went up the entire flight, she walked up some steps and ran up 16 steps. This took a total of 60 seconds.
The second time she went up the entire flight, she walked up some steps and ran up 28 steps. This took a total of 42 seconds. How long would Yazmin take if she walked up the entire flight of steps? (You may assume constant rates for walking and running.)
Professor REINY
I search every inch of question you solved tactically.........
Was wondering if you had come up with any easier way back then though or I'll painfully stick with this....
Wow wow wow
Let
x = number of steps
r = time per running step
w = time per walking step
we have
16r+(x-16)w = 60
28r + (x-28)w = 42
This gives us
w = r + 3/2
x = 168/(2r+3)
Since x is an integer and x≥28, 2r+3 must be a factor of 168 ≤ 6
Since r≥0, only 6 is possible.
If 2r+3=6, then r = 3/2, and w = 3, and there are 28 steps
walking the whole way would take 3*28 = 84 seconds
There is another solution if 2r+3=4, r = 1/2
Then w = 2, and there are 42 steps
walking would again take 84 seconds
This particular question
October 29 2015 this question was posted by DC
You used a computer program to make a perfect guess
Which I don't know how you were able to do it
Didn't even know it showed up as the first entry in "Similar Questions"
Looks like my basic approach is the same in both solutions, I recall making up
such a program in the language of BASIC, and basically letting the computer
try all the different possibilities
Thank you sir reiny....I read it and again and again and I like it
And also sir obleck I understand it much better now thanks man
To find out how long Yazmin would take if she walked up the entire flight of steps, we can use the information given in the question.
Let's assign variables:
Let's say the total number of steps in the flight is "s."
Let's say Yazmin's walking speed is "w" steps per second.
Let's say Yazmin's running speed is "r" steps per second.
From the first part of the question, we know that:
Yazmin walked "x" steps and ran 16 steps, so the total number of steps covered in 60 seconds is (x + 16).
Using the given speeds, we can set up the equation:
(x/w) + (16/r) = 60
From the second part of the question, we know that:
Yazmin walked "y" steps and ran 28 steps, so the total number of steps covered in 42 seconds is (y + 28).
Using the given speeds, we can set up the equation:
(y/w) + (28/r) = 42
Now we have two equations with two unknowns (x and y). We can solve this system of equations to find the values of x, y, w, and r.
Once we have determined the values of w (walking speed) and r (running speed), we can find the time it takes for Yazmin to walk up the entire flight by dividing the total number of steps (s) by her walking speed (w), since she would only be walking in this case.
Please note that without additional information or mathematical simplification, we cannot determine an exact value for the time Yazmin would take if she walked up the entire flight.
total number of steps ---- x
rate of running up the stairs ----- r steps/sec
rate of walking up the stairs ----- w steps/se
Case1: runs 16 steps, walks x-16 steps
16/r + (x-16)/w = 60
16w + r(x-16) = 60rw **
case2: runs 28 steps, walks x-28
28/r + (x-28)/w = 42
28w + r(x-28) = 42 rw ***
divide ** by ***
(16w + r(x-16)) / (28w + r(x-28) ) = = 60rw/(42rw) = 10/7
10(28w) + 10r(x-28) = 112w + 7r(x-16)
280w + 10rx - 280r = 112w + 7rx - 112r
3rx = 168r - 168w
rx = 56r - 56w
time taken to walk all stairs = x/w, so we need to fudge the last equation
rx = 56r - 56w
divide by r
x = 56 - 56w/r
now divide by w
x/w = 56/w - 56/r = 56( 1/w - 1/r)
now I am stuck
had 3 unknowns, but only 2 equations
As to your last part of the post, I don't recall what question you are talking about
Perhaps if you find the time and date it was posted ....