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

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) (Show Source): You can put this solution on YOUR website!
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
+ 1 =
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

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