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put this solution on YOUR website!# 3
Let x = original speed (ie slower speed)
Start with the distance-rate-time formula
Plug in
and
Divide both sides by "x" to isolate "t"
The statement "if he had gone 10mph faster, the trip would have taken 1 hour less" tells us that the new speed is
and the new time is
Go back to the distance-rate-time formula
Plug in
,
, and replace
with
FOIL
Plug in
Multiply
Multiply
every term by the LCD "x" to clear the denominator
Subtract 200x from both sides
Combine like terms
Notice we have a quadratic equation in the form of
where
,
, and
Let's use the quadratic formula to solve for x
Start with the quadratic formula
Plug in
,
, and
Negate
to get
.
Square
to get
.
Multiply
to get
Rewrite
as
Add
to
to get
Multiply
and
to get
.
Take the square root of
to get
.
or
Break up the expression.
or
Combine like terms.
or
Simplify.
So the possible answers are
or
Since a negative speed doesn't make sense, this means that the only solution is
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Answer:
So the original speed was 40 mph
