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

Answer by ankor@dixie-net.com(22740) (Show Source): 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
----------------
difference .4 hrs
RELATED QUESTIONS
If I increase my usual driving speed by 10 km/h, I can drive the 255 km trip to Nashville (answered by ptaylor)

If I increase my usual driving speed by 10 km/h, I can drive the 255 km trip to Nashville (answered by solver91311)

If I increase my usual driving speed by 10 km/h, I can drive the 255 km to Nashviille in... (answered by checkley71)

need to write an equation and solve Julia Ling drove the 200 km to Richmond at a speed (answered by ikleyn)

Helped by a strong jet stream, a Los Angeles-to-Boston plane flew 10% faster than usual... (answered by ewatrrr)

If Alexandra increases her usual driving speed by 15 km/h, it will take her 2h less to... (answered by mananth)

Helped by a strong jet stream, a Los Angeles-to-Boston plane flew 10% faster than usual... (answered by josmiceli)

Amy drove the 200 miles to New Orleans at an average speed 10 miles per hour faster than... (answered by Theo)

Aeroplane left 30 minutes later than its scheduled time and in order to reach distination (answered by josgarithmetic,lwsshak3)