SOLUTION: 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

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Question 1183640: 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.
Answer by ikleyn(52788) About Me  (Show Source):
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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: 


    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%28cross%28expected%29%29 scheduled 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%28cross%28expected%29%29 scheduled time. 
    Find the distance that he had traveled.


                        SOLUTION 


Let d be the distance from the house to the office.


The travel time in the first  scenario is  d%2F2  hours.

The travel time in the second scenario is  d%2F3  hours.


The difference of the travel times is  (t - 8:00 - 3) - ((t+6) - 8:30) = 30 -3 - 6 = 21 minutes, or 21%2F60 of an hour,
where "t" is the scheduled time clock reading.



It gives the time equation


     d%2F2 - d%2F3 = 21%2F60    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.    ANSWER


ANSWER.  The distance from home to the office is  2.1 miles.


CHECK.  The travel time in the first scenario is  2.1%2F2 = 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%2F3 = 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 !

Solved.