SOLUTION: After traveling for 40 minutes, Mr. Koole had to slow to 2/3 his original speed for the rest of the trip due to heavy traffic. The total trip of 84 miles took 2 hours. Find his ori

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Question 1151746: After traveling for 40 minutes, Mr. Koole had to slow to 2/3 his original speed for the rest of the trip due to heavy traffic. The total trip of 84 miles took 2 hours. Find his original speed.
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
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After traveling for 40 minutes, Mr. Koole had to slow to 2/3 his original speed for the rest of the trip due to heavy traffic. The total trip of 84 miles took 2 hours.
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SPEED          TIME hours        DISTANCE

r               2/3             (2/3)r            

(2/3)r          2-2/3=4/3       (2/3)(4/3)r

TOTALS           2                84

cross%28%282%2F3%29r%2B%284%2F3%29r=84%29
.
.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance he traveled
for the first 40 min
+84+-+d+ = distance he traveled for the
remaining time
Let +s+ = his speed for first 40 min
+%282%2F3%29%2As+ = his speed for remaining time
----------------------------------------------------
(1) +d+=+s%2A%28+40%2F60+%29+
(2) +84+-+d+=+%28+%282%2F3%29%2As+%29%2A%28+2+-+%282%2F3%29+%29+
----------------------------------------------------
(1) +d+=+%282%2F3%29%2As+
and
(2) +84+-+d+=+%28+4%2F3+%29%2A%28+2%2F3+%29%2As+
(2) +84+-+d+=+%28+8%2F9+%29%2As+
(2) +84+-+%28+6%2F9+%29%2As+=+%28+8%2F9+%29%2As+
(2) +%2814%2F9%29%2As+=+84+
(2) +s+=+54+
His original speed was 54 mi/hr
------------------------------------
check:
+d+=+%282%2F3%29%2As+
+d+=+%282%2F3%29%2A54+
+d+=+36+ mi
and
(2) +84+-+d+=+%28+8%2F9+%29%2As+
(2) +84+-+d+=+48+
(2) +d+=+36+ mi
OK

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
After traveling for 40 minutes, Mr. Koole had to slow to 2/3 his original speed fFor the rest of the trip due to heavy traffic.
The total trip of 84 miles took 2 hours. Find his original speed.
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            The setup and the setup equation in the post by @josgarithmetic are  INCORRECT.

            So,  I came to provide a correct solution.

            For your safety,  simply ignore the post by  @josgarithmetic. 


SPEED          TIME hours        DISTANCE

r               2/3             (2/3)r            

(2/3)r          2-2/3=4/3       (4/3)(2/3)r = (8/9)r

TOTALS           2                84


Equation


%282%2F3%29r + %288%2F9%29r = 84


Multiply by 9 both sides


6r + 8r = 9*84

14r     = 9*84

  r     = 9%2A%2884%2F14%29 = 9*6 = 54.


ANSWER.  The original speed was  54 miles per hour.

Solved.