SOLUTION: pat rode 30 miles. bob covered twice distance adding one hour and going five miles faster per hour. what was speed of each

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Question 287904: pat rode 30 miles. bob covered twice distance adding one hour and going five miles faster per hour. what was speed of each
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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pat rode 30 miles. bob covered twice distance adding one hour and going five
miles faster per hour. what was speed of each
:
Let s = Pat's speed
then
(s+5) = Bob's speed
:
Write a time equation: Time = Distance/speed
:
Pat's time + 1 hr = Bob's time
30%2Fs + 1 = 60%2F%28%28s%2B5%29%29
multiply by s(s+5), results:
30(s+5) + s(s+5) = 60s
:
30s + 150 + s^2 + 5s = 60s
:
s^2 + 30s + 5s - 60s + 150 = 0
:
s^2 - 25s + 150 = 0
Factor
(s - 10)(s - 15) = 0
Two solutions
s = 10 mph is Pat's speed; then Bob = 15 mph
and
s = 15 mph is Pat's speed; then Bob = 20 mph
:
:
Check both solutions by finding the times for each (should be a 1hr difference)
Bob: 60/15 = 4 hr
Pat: 30/10 = 3 hr
and
Bob: 60/20 = 3 hr
Pat: 30/15 = 2 hr