SOLUTION: a man gets 20 minutes late to his office when he travels at a speed of 20 kmph and 25 mins. Early when he travels at a speed of 80 kmph. The distance he travels to reach his office

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Question 837670: a man gets 20 minutes late to his office when he travels at a speed of 20 kmph and 25 mins. Early when he travels at a speed of 80 kmph. The distance he travels to reach his office is
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
He begins at a time point on a time line. He can go slow and be t%2B1%2F3 hours or he can go fast and be t-25%2F60=t-5%2F12 hours. The variable, t is used as a reference to time on a number line.


______________speed________time(hours)_____distance(km)
Slow,late_______20________t+1/3_____________d
Fast,early______80________t-5/12____________d


The distance is the same value for both speeds used, early or late.

Rate%2ATime=Distance, basic concept.
highlight%2820%28t%2B1%2F3%29=80%28t-5%2F12%29%29
If everything makes sense to this extent, then you are ready to solve for t. This is the value the man expects if to arrive ON-TIME.
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20t%2B20%2F3=80t-80%2A5%2F12
20%2F3%2B80%2A5%2F12=60t
80%2F12%2B400%2F12=60t
480%2F12=60t
40=60t
t=4%2F6
highlight%28t=2%2F3%29 hour which is 40 minutes.
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Now, what is the distance?
Either direction's equation will work. Trying the slow form,
d=20%28t%2B1%2F3%29
d=20%282%2F3%2B1%2F3%29
d=20%2A1
highlight%28highlight%28d=20%29%29 km