SOLUTION: Johnny was able to drive an average of 17 miles per hour faster in his car after the traffic cleared. He drove 46 miles in traffic before it cleared and then drove another 80 miles

Question 1103054: Johnny was able to drive an average of 17 miles per hour faster in his car after the traffic cleared. He drove 46 miles in traffic before it cleared and then drove another 80 miles. If the total trip took 4 hours, then what was the average speed in traffic?
Found 2 solutions by ankor@dixie-net.com, KMST:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Johnny was able to drive an average of 17 miles per hour faster in his car after the traffic cleared.
He drove 46 miles in traffic before it cleared and then drove another 80 miles.
If the total trip took 4 hours, then what was the average speed in traffic?
:
let s = speed in traffic
(s+17) = out of traffic
:
Write a time equation; time = dist/speed
traffic time + normal speed time = 4 hrs
+ = 4
multiply by s(s+17) to cancel the denominators
46(s+17) + 80s = 4s(s+17)
46s + 782 + 80s = 4s^2 + 68s
126s + 782 = 4s^2 + 68s
Arrange as a quadratic equation on the right
0 = 4s^2 + 68s - 126s - 782
4s^2 - 58s - 782 = 0
simplify, divide by 2
2s^2 - 29s - 391 = 0
Use the quadratic formula a=2; b=-29; c=-391
I got a positive solution of
s = 23 mph in traffic
:
:
:
Check this by finding the actual times. Normal speed: 23 + 17 = 40 mph
46/23 = 2 hrs in traffic
80/40 = 2 hrs at normal speed
----------------------------
total time 4 hrs

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If you prefer to solve quadratic equations by factoring,
with = average speed in traffic, in mph,

The positive solution, from is

To get the coefficients for the terms
and that add up to ,
we look for two numbers
whose product is ,
and whose sum is .
does not work, because ,
but works, because .
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