SOLUTION: Amanda leaves Boston at 10:00 AM and drives to Buffalo, NY, which is 400 miles away. After 4 hours, the traffic causes Amanda to reduce her speed by 20 mph. She stops to rest for t

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Amanda leaves Boston at 10:00 AM and drives to Buffalo, NY, which is 400 miles away. After 4 hours, the traffic causes Amanda to reduce her speed by 20 mph. She stops to rest for t      Log On

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Question 1167511: Amanda leaves Boston at 10:00 AM and drives to Buffalo, NY, which is 400 miles away. After 4 hours, the traffic causes Amanda to reduce her speed by 20 mph. She stops to rest for two hours, and then arrives in Buffalo at 8:00 PM.
What was Amanda's initial speed?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "r" be the initial speed, in miles per hour.

Then the lower speed was (r-20) mph.


The total driving time was 10 hour from 10:00 am to 8:00 pm minus 2 hour for the rest = 8 hours.


Of them, 4 hours she drove at the rate r mph, and the remaining 8 - 4 = 4 driving hours at the lower rate (r-20) mph.


The total distance equation is

    4*r + 4*(r-20) = 400


Simplify and solve

    4r + 4r - 80 = 400

    8r           = 400 + 80 = 480

     r                      = 480/8 = 60 mph.


ANSWER.  The initial speed / (rate) was 60 mph.

Solved.

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    - Travel and Distance problems for two bodies moving in opposite directions
    - Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.

They are written specially for you.

You will find the solutions of many similar problems there.

Read them and learn once and for all from these lessons on how to solve simple Travel and Distance problems.

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Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


You should know how to solve the problem using formal algebra, as shown by the other tutor.

However, if a formal algebraic solution is not required, and/or if you want to get some good practice in logical thinking (and thus give your brain some good exercise), this problem lends itself to a quick and easy solution.

The total trip was 10 hours; she stopped for a rest for 2 hours, so the total driving time was 8 hours.

So her average speed was 400/8 = 50 mph.

She drove for 4 hours at her original speed, so she drove for 4 hours at the reduced speed.

Since she drove equal amounts of time at the two speeds, her overall average of 50 mph was halfway between her two driving speeds.

Since the difference between the two speeds was 20 mph, an overall average of 50 mph means the two speeds were 50+10=60 and 50-10=40 mph.

ANSWER: Her original speed was 60 mph.

CHECK:
4 hours at 60 mph, plus 4 hours at 40 mph, equals 400 miles
4(60)+4(40) = 240+160 = 400