SOLUTION: Hi A man walks at 4/5 of his speed to his office and is late by 5 min. What is the time it takes to reach his office if he walks at 3/4 of his speed. Thanks

Question 1156576: Hi
A man walks at 4/5 of his speed to his office and is late by 5 min. What is the time it takes to reach his office if he walks at 3/4 of his speed.
Thanks
Answer by ikleyn(52767) (Show Source): You can put this solution on YOUR website!
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The original formulation in the post is FAR from to be PERFECT.

The PERFECT and PRECISELY CORRECT formulation is THIS:

    A man walks at 4/5 of his speed to his office and is late by 5 min. 
    What is the time it takes to reach his office if he walks at 3/4 of his  speed.

I will solve the problem with this formulation.

Let "d" be the distance to the office, and let "u" be the regular speed.


Then the condition produces this time equation

     -  = 5 minutes.


Simplify

     -  = 5 minutes,   or

     = 5 minutes,   or

      = 4*5 = 20 minutes.


So, his REGULAR time to get the office is 20 minutes.


Now, if he moves at    of his refular speed, it will take   =  =  minutes = 26 minutes and 40 seconds

to get the office.     ANSWER

Solved.

Same idea can be presented in other form.

Let T be the regular time to get the office (moving at regular speed).


Then with the speed of   of the regular, the time will be  .

Then the condition says us that

     - T = 5 minutes,  or

     = 5 minutes,

which means  T = 4*5 = 20 minutes (regular time).


Then with the speed of    of the regular, the time will be   =  = 26 minutes and 40 seconds (the same answer).

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