SOLUTION: A person covers a certain distance on car. Had he moved 30 km/hr faster, he would have taken 2.5 hrs less. If he has moved 10 km h slower, he would have taken 2.5hrs more. What is

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Question 983571: A person covers a certain distance on car. Had he moved 30 km/hr faster, he would have taken 2.5 hrs less. If he has moved 10 km h slower, he would have taken 2.5hrs more. What is his original speed.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
                speed        time       distance    EQUATIONS
NORMAL           r            t          d          rt=d
FASTER          r+30         t-2.5       d          (r+30)(t-2.5)=d
SLOWER          r-10         t+2.5       d          (r-10)(t+2.5)=d


Additional equation might help:          (r+30)(t-2.5)=(r-10)(t+2.5)


-
FAST equation
rt%2B30t-2.5r-75=d
d%2B30t-2.5r-75=d
30t-2.5r-75=0
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SLOW equation
rt-10t%2B2.5r-25=d
-10t%2B2.5r-25=0
-
The additional equation in the table is not necessary.

The equations as found can be simplified for convenience if multiply each by 2.
Those as a system of equations:
system%2860t-5r-150=0%2C-20t%2B5r-50=0%29
and then further
system%2812t-r-30=0%2C4t-r%2B10=0%29

Elimination Method is perfectly convenient for the system.
12t-r-30-%284r-r%2B10%29=0-0
8r-30-10=0
8r=40
highlight%28highlight%28r=5%29%29

Answer by MathTherapy(10810) About Me  (Show Source):
You can put this solution on YOUR website!

A person covers a certain distance on car. Had he moved 30 km/hr faster, he would have taken 2.5 hrs less. If he has moved 10 km h slower, he would have taken 2.5hrs more. What is his original speed.
Original speed: highlight_green%2830%29 km/h