SOLUTION: Q: Bob and Bill both drive 60 miles to work. Bill drives an average of 10 miles per hous faster than Bob and it takes Bill 12 minutes less than Bob to get there. How fast are they

Question 393348: Q: Bob and Bill both drive 60 miles to work. Bill drives an average of 10 miles per hous faster than Bob and it takes Bill 12 minutes less than Bob to get there. How fast are they driving?

I just have no idea what kind of porportion I should be setting up. I've tried to think this through logically but I can't figure it out. Thank you for whatever help you can provide
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Q: Bob and Bill both drive 60 miles to work.
Bill drives an average of 10 miles per hrs faster than Bob and it takes
Bill 12 minutes less than Bob to get there.
How fast are they driving?
:
Lets do it this way.
:
Let s = Bob's speed
then
(s+10) = Bill's speed
:
Change 12 min to .2 hrs
:
Write a time equation: Time = dist/speed
:
Bob's time - Bills time = .2 hrs
- = .2
Multiply by s(s+10); results:
60(s+10) - 60s = .2s(s+10)
:
60s + 600 - 60s = .2s^2 + 2s
An quadratic equation
.2s^2 + 2s - 600 = 0
Multiply by 5 to get rid of the decimal
s^2 + 10s - 3000 = 0
Factors to
(s+60)(s-50) = 0
the positive solution:
s = 50 mph is Bob's speed, then obviously 60 mph is Bill's speed
:
:
See if this is true, find the travel time of each
60/50 = 1.2 hrs
60/60 = 1.0 hrs
---------------
differs: .2 hrs
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