SOLUTION: On a recent trip, a trucker traveled 525 mi at a constant rate. Because of road conditions, the trucker then reduced the speed by 30 mph. An additional 45 mi was traveled at the re

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Question 1205546: On a recent trip, a trucker traveled 525 mi at a constant rate. Because of road conditions, the trucker then reduced the speed by 30 mph. An additional 45 mi was traveled at the reduced rate. The entire trip took 8 h. Find the rate of the trucker for the first 525 mi.
mph
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
This is the information that can be arranged from the problem description; and the constant speed for the first part is unknown, x.
                                  SPEED                 TIME              DISTANCE

Constant Rate                     x                                       525

Reduced Speed                    x-30                                      45

TOTAL                                                      8

Use that to fill other information.
                                      SPEED                 TIME              DISTANCE

Constant Rate                        x                      525/x                 525

Reduced Speed                         x-30                 45/(x-30)              45

TOTAL                                                          8

Solve this equation: highlight_green%28525%2Fx%2B45%2F%28x-30%29=8%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

On a recent trip, a trucker traveled 525 mi at a constant rate.
d=rt
t=d/r
t=525%2Fr
Because of road conditions, the trucker then reduced the speed by 30 mph.
%28r-30%29
An additional 45 mi was traveled at the reduced rate.
t=45%2F%28r-30%29
The entire trip took 8 h.
8=525%2Fr%2B45%2F%28r-30%29
8%28r-30%29=525%28r-30%29%2Fr%2B45
8r-240=%28525+r+-+15750%29%2Fr%2B45...multiply by r
8r%5E2-240r=525+r+-+15750%2B45r
8r%5E2-240r-525+r+%2B15750-45r=0
8+r%5E2+-+810+r+%2B+15750=0
2+%28r+-+75%29+%284+r+-+105%29+=+0

r=75+
or
r=105%2F4=26.25....disregard because speed was reduced by 30mph

so, the rate of the trucker for the first 525 mil was 75mph