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.Com
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(52781)   (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.

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

For simple Travel & Distance problems,  see introductory lessons
    - Travel and Distance problems
    - 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.

Become an expert in this area.




Answer by greenestamps(13200)   (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
RELATED QUESTIONS

Wilma drove at an average speed of 50 mi/h from her home in Boston to visit her sister in (answered by lwsshak3,Alan3354)
Trian A leaves Bosotn for NY at 7 am going 30mph. Trian B leaves NY for Boston at 8:30 am (answered by stanbon,ankor@dixie-net.com)
1: stephanie leaves school at 3:00 on her bike and travels at a speed of 10mph. if her... (answered by TimothyLamb)
Amanda leaves her home at 10:00 A.M and needs to get to a meeting 90 mi away by 11:30... (answered by Alan3354)
A train leaves New York for Boston, 200 miles away, at 4:00 P.M. and averages 60 mph.... (answered by drk)
A train leaves New York for Boston, 200 miles away, at 4:00 P.M. and averages 65 mph.... (answered by josmiceli)
A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 50 mph.... (answered by richwmiller)
A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 40 mph.... (answered by richwmiller)
A train leaves New York for Boston, 200 miles away, at 3:00 P.M. and averages 40 mph.... (answered by ewatrrr)