SOLUTION: A trucker calculates that if he increased his average speed by 90 km/h, he could travel his 660-km route in 7 h less time than his usual. Find his usual speed (km/h).

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Question 724611: A trucker calculates that if he increased his average speed by 90 km/h,
he could travel his 660-km route in 7 h less time than his usual.
Find his usual speed (km/h).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Let r = the unknown usual speed.

______________rate______________time___________________distance
Usual_________r_________________t______________________660
Faster_______r+90______________t-7____________________660

We want to solve for r, but t is also a variable and unknown. Fortunately, the rows of data use the SAME distance. We can solve for the times in terms of distance and rates. rate*time=distance.

t=660/r, so t-7=660/r-7.

______________rate______________time___________________distance
Usual_________r_________________660/r______________________660
Faster_______r+90______________660/r-7____________________660
The "Faster" data may be of use. %28r%2B90%29%2A%28660%2Fr-7%29=660

... WAIT!
... Interrupting that, there are TWO equations possible:
rt=660
%28r%2B90%29%28t-7%29=660
Going ahead with that system, the second equation becomes
rt-7r%2B90t-630=660
rt%2B90t-7r=30

and from the first equation, find that t=660/r and substitute to get
r%28660%2Fr%29%2B90%28660%2Fr%29-7r=30
660%2B90%2A660%2Fr-7r=30
660r%2B90%2A660-7r%5E2=30
-7r%5E2%2B660r%2B90%2A660-30=0
-7r%5E2%2B660r%2B59370=0
highlight%287r%5E2-660r-59370=0%29
Using general solution to quadratic equation, highlight%28r=150%29 km/hr

I have not yet tried to check that solution.