SOLUTION: A teacher drove 280 miles to attend a conference and arrived 1 hour late. The teacher calculated that had she increased her average speed by 5 miles per hour, she would have arrive

Question 1054463: A teacher drove 280 miles to attend a conference and arrived 1 hour late. The teacher calculated that had she increased her average speed by 5 miles per hour, she would have arrived on time. What was her average speed?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = time in hrs the teacher takes
when she arrives on time
Let = her speed in mi/hr when she
arrives hr late
---------------------------------------
Equation for arriving 1 hr late:
(1)
Equation for arriving on time:
(2)
-------------------------------
(1)
and
(2)
(2)
Multiply both sides by
(2)
(2)
(2)
(2)
complete the square
(2)
(2)
(2)
(2)
(2)
(2)
(2) ( can only use positive time here )
( cannot use negative square root of )
(1)
(1)
(1)
(1)
Her average speed when arriving 1 hr late was 35 mi/hr
------------------
check answer:
Equation for arriving on time:
(2)
(2)
(2)
(2) hrs
OK

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

A teacher drove 280 miles to attend a conference and arrived 1 hour late. The teacher calculated that had she increased her average speed by 5 miles per hour, she would have arrived on time. What was her average speed?

Let average speed to cover distance be S
Then hypothetical speed = S + 5
We then get the following TIME equation:
280(S + 5) = 280S + S(S + 5) ------- Multiplying by LCD, S(S + 5)

(S � 35)(S + 40) = 0
S, or OR S = - 40 (ignore)
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