SOLUTION: I I increase my usual driving speed by 10 km/h, I can drive the 255 km trip to Nashville in 24 min less than usual. How fast do I usually drive? PLEASE HELP!!!! There is not an ans
Question 122105This question is from textbook algebra: structure and Method: book 1
: I I increase my usual driving speed by 10 km/h, I can drive the 255 km trip to Nashville in 24 min less than usual. How fast do I usually drive? PLEASE HELP!!!! There is not an answer in the back, and I also don't know what to do!!!!HELP!!!!!!!!!!!!!!!!!!! I am sorry if this is not enough info, but that is all there is in the book. This question is from textbook algebra: structure and Method: book 1
You can put this solution on YOUR website! If I increase my usual driving speed by 10 km/h, I can drive the 255 km trip to Nashville in 24 min less than usual. How fast do I usually drive?
:
Let x = the usual driving speed
then
(x+10) = the increased driving speed
:
Convert 24 min to hrs: = .4 hrs
:
Write a time equation: Time =
:
Usual time = faster time + .4 hrs = + .4
:
Multiply the equation by x(x+10) to get rid of the denominators; results:
255(x+10) = 255x + .4(x(x+10)
:
255x + 2550 = 255x = .4x^2 + 4x
:
0 = 255x - 255x + .4x^2 + 4x - 2550
:
.4x^2 + 4x - 2550 = 0
:
Get rid of the decimal and make the coefficient of x^2 = 1
Multiply equation by 2.5 and you have:
:
1x^2 + 10x - 6375 = 0
:
This will factor to:
(x + 85)(x - 75) = 0
:
Positive solution only needed here:
x = 75 km/h is his usual speed
:
:
Check our solution by finding the time difference between the two scenarios
255/75 = 3.4 hrs
255/85 = 3.0 hrs
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difference .4 hrs
