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).

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) (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.

... WAIT!
... Interrupting that, there are TWO equations possible:

Going ahead with that system, the second equation becomes

and from the first equation, find that t=660/r and substitute to get

Using general solution to quadratic equation, km/hr

I have not yet tried to check that solution.

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