Expert: Sherman D. - 10/11/2007

Question
QUESTION: Hello,
I noticed that you have a very high rate of answering questions.  Can you help me with the problem below?
A businessman drives from Washington, D.C. to Boston, a distance of 442 miles, and then makes the return trip.  On the way to Boston, he drives 65 miles per hour, taking a 1-hour rest stop during the drive.  After finishing his business in Boston, he makes the return trip driving at 60 miles per hour and takes a 45-minute rest stop halfway through the trip.

Which leg of the journey, Washington, D.C. to Boston, or Boston to Washington, D.C. takes the longer time?



ANSWER: To Boston
65 = 442/x
x = 442/65
x = 6 hours and 48 minutes
don't forget to add the 1 hour of time

To Boston = 7 hours and 48 minutes

-------------------------------------

To Washington D.C.
y = 442/60
y = 7 hours and 22 minutes
don't forget to add the 45 minutes

To Washington D.C. = 7 hours and 67 minutes or 8 hours and 7 minutes

if i have this correct, and if his speed remains constant even after the rest stops, then the answer is

From Boston To Washington D.C. takes 1 hour and 19 minutes longer.

---------- FOLLOW-UP ----------

QUESTION: I didn't know how do find you again, without having to chose the follow-up question.  I was wondering if you can help me with another problem, if you have time.
I have to perform the following sums without using a calculator.  It's been a while since I had to do math this way, so I'm kind of lost with these problems.
 241
- 177
What would be the sum?

ANSWER: are you asking for 241 + (-177) = 241 - 177 = 64

---------- FOLLOW-UP ----------

QUESTION: No, not 241 +(-177),
I'm asking 241-177.  Using the standard line up when subtracting. Example:  241
         - 177
Remember, I can't use a calculator for this.

Answer
if you are asking 177 subtracted from 241, which 241 - 177 is the same as 241 + (-177) = 64

```13
`1`3`11
`2`4`1
-1`7`7
-----
  6`4

the numbers at the top of the actual numbers is what they become. the first top is what the become first and the ones at the very top become what the first top will become.

now if you are asking, add the numbers from 241 to 177

then mathematically, this is quite easy

an = 241 - (n - 1) = 241 - n + 1 = 242 - n
to get from 241 to 177 is 65 numbers

Sn = (n/2)(a1 + an)
S(65) = (65/2)(241 + 177)
S(65) = 32.5 * 418
S(65) = 13585

if you add from 241 to 177, i GUARANTEE you will get 13585 because i checked it myself.

info found at http://www.ltcconline.net/greenl/Courses/103B/seqSeries/ARITSEQ.HTM

i hope that was what you were looking for.