SOLUTION: If the speed were increased by 10mph, a 420-mile trip would take 1 hour less time. How long will the trip take at the slower speed?
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Question 988383: If the speed were increased by 10mph, a 420-mile trip would take 1 hour less time. How long will the trip take at the slower speed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If the speed were increased by 10mph, a 420-mile trip would take 1 hour less time.
How long will the trip take at the slower speed?
:
let s = the slower speed
then
(s+10) = the faster speed
:
Write a time equation; time = dist/speed
:
slo speed time - fast speed time = 1 hr
- = 1
multiply equation by s(s+10), cancel the denominators
420(s+10) - 420s = s(s+10)
420s + 4200 - 420s = s^2 + 10s
Combine to form a quadratic equation
s^2 + 10s - 4200 = 0
You can use the quadratic formula to find s, but this will factor to
(s+70)(s-60) = 0
The positive solution is what we want here
s = 60 mph is the slower speed
"How long will the trip take at the slower speed?"
= 7 hrs
:
:
We can confirm this solution by finding the time at the faster speed
420/70 = 6 hrs, one hr less
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