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Re: SAT and the AT

>> Christina,
>> >23. excluding rest stops, it took juanita a total of 10
>> >hours to hike from the base of a mountain to the top
>> >and back down again by the same path (could this be >Katahdin?).
>> > if while hiking she averaged 2 miles per hour going up and
>> >3 miles per hour going down, how many miles was it from the
>> >base to the top?
>> >a)8
>> >b)10
>> >c)12
>> >d)20
>> >e)24
>It's 12, isn't it?
>let x=distance up (&down)
> then    x / 2 mph = time up
>   &     x / 3 mph = time dn
>put it all togeather to get :  x/2 + x/3 = 10hrs.
>multiply each value in the equation by 6(least common multiple?) to get
> 3x+2x=60  or 5x=60  or x=60/5=12

I am an SAT instructor and although I am a PA math teacher (you know,
Pennsylvania -- which ranked 15th among the states in this country on an
*International* Math Proficeny scale, despite claims by someone on this
list), I would not have solved that problem algebraically.

It is far easier to solve it arithmetically using the answers.  For example
start with 12 (the median (middle) of the five numbers).  Two mph up would
be 6 hours, three mph down would be 4 hours -- 6 + 4 = 10.  Finito -- move

For the record, suppose the median was 8 and you tried 8 as the answer.
Two mph up would take 4 hours, 3 miles per hour down would be 2 plus some
more (2/3 to be exact), which adds to a little more than 6.  Too short --
pick a large number and move to 10 or 12 unless you notice that the answer
must be a multiple of 2 and 3, in which case you would eliminate 10 and try

Good luck to whomever is taking the test!

"FOR DUTY & HUMANITY" -- Dr. Howard, Dr. Fine, Dr. Howard