SOLUTION: At the​ airport, Person A and Person B are walking at the same speed to catch their​ flight, but Person B decides to step onto the moving​ sidewalk, while Person A continues

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Question 1138861: At the​ airport, Person A and Person B are walking at the same speed to catch their​ flight, but Person B decides to step onto the moving​ sidewalk, while Person A continues to walk on the stationary sidewalk. If the sidewalk moves at 1 meter per​ second, and it takes Person B 30 seconds less to walk the 360​-meter ​distance, at what speed are Person A and Person B​ walking?
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
Let x be the speed of A and B (the same (!) ) walking on the stationary sidewalk (in meters per second).

Then the effective speed of B on the moving sidewalk is (x+1) m/s.


The time equation is 


     -  = 30 seconds.


Cancel the factor of 30 in both sides and then multiply both sides by x*(x+1).


    12(x+1) - 12x = x*(x+1)

    12            = x^2 + x

     x^2 + x - 12 = 0

     (x+4)*(x-3) = 0.


The roots are x= -4  and  x= 3, but only positive value x= 3 is the meaningful solution.


ANSWER.  The speed of A and B walking on stationary sidewalk is 3 meters per second.


CHECK.    -  = 120 - 90 = 30 seconds.   ! Correct !

Solved. 

     (Actually, it is very high speed for walking person.

      Usual speed walking is about 1 m/s, as everybody knows.

      I suspect that it would be much more realistic to have feet in this problem instead of meters !)

--------------------

Using "time" equation is the STANDARD method of solving such problems.

To see many other similar solved problems by this method,  look into the lessons
    - Had a car move faster it would arrive sooner
    - How far do you live from school?
    - Earthquake waves
    - Time equation: HOW TO use, HOW TO write and HOW TO solve it
in this site.

From these lessons,  learn on how to write,  how to use and how to solve a  "time"  equation.


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