SOLUTION: Hi If speed is increased by 20 percent a person arrives 15 minutes early. What is the initial time taken by the person. Thanks

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Question 1186798: Hi
If speed is increased by 20 percent a person arrives 15 minutes early. What is the initial time taken by the person.
Thanks
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the initial time t
the initial speed s+
if speed is increased by 20 percent :
s%2B0.20s
time reduced 15 min
t-15

st=%28s%2B0.20s%29%28t-15%29
st=1.2+s+%28t+-+15%29
t=1.2t+-+18
18=1.2t+-+t
18=0.2t+
t=18%2F0.2
t=90min ->the initial time taken by the person

Answer by ikleyn(52793) About Me  (Show Source):
You can put this solution on YOUR website!
.
If speed is increased by 20 percent, a person arrives 15 minutes highlight%28cross%28early%29%29 earlier.
What is the highlight%28cross%28initial%29%29 regular time taken by the person.
~~~~~~~~~~~~~~~~~ 


Let  "d"  be the distance, let "t" be the regular (= the scheduled) travel time (in minutes), and let "u"  be the regular speed. 

Then the increased speed is  1.2u, and reduced traveled time is  t-15 minutes.


We have two equations

    d%2Fu = t              (1)

and

    d%2F%281.2u%29 = t - 15    (2)


From equation (2), we have

    d%2Fu = 1.2*(t-15).


In this equation, replace its left side  d%2Fu  by  t, based on equation (1).  
You will get then simple linear equation for the single unknown t


    t = 1.2*(t-15).


Simplify and find t

    t = 1.2t - 18

    18 = 1.2t - t

    18 = 0.2t

     t = 18%2F0.2 = 180%2F2 = 90 minutes.


ANSWER.  The regular (=the scheduled) travel time is 90 minutes.

Solved.