Question 55944: Anna visited her Aunt in a town which is 220 miles from where Anna lives. On her way to her Aunt's town she had to slow down for 70 miles where one of the lanes was closed due to a traffic accident. If she had to slow down by 15 mph and the trip took her 5 hours, find the speed at which she drove on the one lane portion. (Hint: after establishing your equation as a rational equation, convert it into a quadratic equation).
I come up with an average speed of 44mph, however I can't figure out if this is useful for solving the problem. I am lost.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Anna visited her Aunt in a town which is 220 miles from where Anna lives. On her way to her Aunt's town she had to slow down for 70 miles where one of the lanes was closed due to a traffic accident. If she had to slow down by 15 mph and the trip took her 5 hours, find the speed at which she drove on the one lane portion. (Hint: after establishing your equation as a rational equation, convert it into a quadratic equation).
:
Let s = Her 1 lane speed
The time she traveled at this speed = 70/s
:
Then (s+15) = her speed the rest of the trip
The time she traveled at this speed = (220-70)/(s+15)
:
Slow speed time + fast speed time = 5 hr
70/s + 150/(s+15) = 5
:
Mult equation by s(s+15) and you have:
70(s+15) + 150s = 5(s(s+15)
70s + 1050 + 150s = 5s^2 + 75s
0 = 5s^2 + 75s - 70s - 150s - 1050
:
The quadratic equation, that we so earnestly seek:
5s^2 - 145s - 1050 = 0
:
Simplify, divide by 5
s^2 - 29s - 210 = 0
:
Factors to:
(s + 6)(s - 35) = 0
:
s = + 35 mph speed on the 1 lane road
:
Use the two speeds (normal highway 50 mph) to check our solution
70/35 + 150/50 = 5 hr
.
|
|
|
