SOLUTION: they traveled the first 70 miles at a constant rate of speed for the remainder of the trip they ran into bad weather, and had to reduce speed by 30 mph for the last 12 miles of the

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Question 1118332: they traveled the first 70 miles at a constant rate of speed for the remainder of the trip they ran into bad weather, and had to reduce speed by 30 mph for the last 12 miles of the trip. The trip took 2 hours. Find the rate of speed for each part of the trip.
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This is a trip of how many - two parts? 
                 SPEED     TIME      DISTANCE

FirstPart          r       70/r        70

LastPart          r-30     12/(r-30)   12

ALL                           2

Solve for r and evaluate r-30;
highlight_green%2870%2Fr%2B12%2F%28r-30%29=2%29

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
They traveled the first 70 miles at a constant rate of speed
for the remainder of the trip they ran into bad weather, and had to reduce speed by 30 mph for the last 12 miles of the trip.
The trip took 2 hours.
Find the rate of speed for each part of the trip.
:
Let s = the original speed
then
(s-30) = the slower speed
:
Write a time equation: time = dist/speed
70%2Fs + 12%2F%28%28s-30%29%29 = 2
multiply equation by s(s-30)
s(s-30)* 70%2Fs + s(s-30)*12%2F%28%28s-30%29%29 = 2s(s-30)
Cancel the denominators
70(s-30) + 12s = 2s^2 - 60s
70s - 2100 + 12s = 2s^2 - 60s
82s - 2100 = 2s^2 - 60s
0 = 2s^2 - 60s - 82s + 2100
2s^2 - 142s + 2100 = 0
simplify, divide 2
s^2 - 71s + 1050 = 0
You can use the quadratic formula, but this will factor to
(s-50)(s+21) = 0
s = 50 mph for the first 70 mi
then
50 - 30 = 20 mph for the last 12 hrs
;
:
:
Check, find the actual time at each speed
70/50 = 1.4 hrs
12/20 = .6 hrs
-----------------
trip time: 2 hrs