Question 393348
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
{{{60/s}}} - {{{60/((s+10))}}} = .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
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differs: .2 hrs