Question 1183640
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A man leaves his house at 8:00 AM and traveling at an average speed of 2 kph, arrives at his office 
3 min ahead of the expected time. Had he left his house at 8:30 am and traveled at an average speed of 3 kph, 
he will arrive 6 min late of the expected time. Find the distance that he had traveled.
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            As the problem is worded,  it may perplex the reader.

            To avoid perplexing,  I'd re-formulate the condition this way:



<pre>
    A man leaves his house at 8:00 AM and traveling at an average speed of 2 kph, arrives at his office 
    3 min ahead of the {{{highlight(cross(expected))}}} <U>scheduled</U> time. 
    Had he left his house at 8:30 am and traveled at an average speed of 3 kph, 
    he will arrive 6 min late of the {{{highlight(cross(expected))}}} <U>scheduled</U> time. 
    Find the distance that he had traveled.
</pre>


     &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>SOLUTION</U>



<pre>
Let d be the distance from the house to the office.


The travel time in the first  scenario is  {{{d/2}}}  hours.

The travel time in the second scenario is  {{{d/3}}}  hours.


The difference of the travel times is  (t - 8:00 - 3) - ((t+6) - 8:30) = 30 -3 - 6 = 21 minutes, or {{{21/60}}} of an hour,
where "t" is the scheduled time clock reading.



It gives the time equation


     {{{d/2}}} - {{{d/3}}} = {{{21/60}}}    hours


to find "t".   To solve the equation, multiply both sides by 60.  You will get


    30d - 20d = 21

       10d    = 21

        d     = 21/10 = 2.1 miles.    <U>ANSWER</U>


<U>ANSWER</U>.  The distance from home to the office is  2.1 miles.


<U>CHECK</U>.  The travel time in the first scenario is  {{{2.1/2}}} = 1.05 hours = 1 hour and 3 minute.

        Hence, the appointment time (scheduled arriving time) is 9:06 am.


        In the second scenario, his travel time was  {{{2.1/3}}} = 0.7 of an hour, or 42 minutes; 
                                he started at 8:30 am, hence, he arrived at 9:12 am, which is  6 minutes later 
                                than the scheduled arriving time of 9:06 am.

        ! Correct !
</pre>

Solved.