SOLUTION: mr. robinson traveled to a city 260 miles from his home to attend a meeting. due to car trouble, his average speed returnting was 5 mpg less than his speed going. if the total time

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Question 983131: mr. robinson traveled to a city 260 miles from his home to attend a meeting. due to car trouble, his average speed returnting was 5 mpg less than his speed going. if the total time for the round trip was 12 hours, at what rate of speed did he travel to the city?( round off your answer to the nearest tenth.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
_________________rate____________time_____________distance
ToCity____________r______________(___)_____________260
ToHome___________r-5_____________(___)_____________260
TOTAL_____________________________12


_________________rate____________time_____________distance
ToCity____________r______________260/r_____________260
ToHome___________r-5_____________260/(r-5)_________260
TOTAL_____________________________12


260%2Fr%2B260%2F%28r-5%29=12


260%281%2Fr%2B1%2F%28r%2B5%29%29=12

65%281%2Fr%2B1%2F%28r%2B5%29%29=3

65%28r%2B5%2Br%29=3r%28r%2B5%29

3r%5E2%2B15r=65%2A2r%2B65%2A5

3r%5E2%2B15r=130r%2B325

3r%5E2-130r-325=0------not factorable; ...

r=%28130%2B-+sqrt%28130%5E2-4%2A3%2A%28-325%29%29%29%2F%282%2A3%29

r=%28130%2B-+sqrt%2820800%29%29%2F%282%2A3%29

r=%28130%2B-+10%2Asqrt%28208%29%29%2F%282%2A3%29

r=%2865%2B-+5%2Asqrt%28208%29%29%2F3

r=%2865%2B-+20%2Asqrt%2813%29%29%2F3, you must use the POSITIVE value.

highlight%28r=%2865%2B20%2Asqrt%2813%29%29%2F3%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

mr. robinson traveled to a city 260 miles from his home to attend a meeting. due to car trouble, his average speed returnting was 5 mpg less than his speed going. if the total time for the round trip was 12 hours, at what rate of speed did he travel to the city?( round off your answer to the nearest tenth. 
Equation formed: 3S%5E2+-+145S+%2B+325++=+0, with S being speed

Speed to city: 45.97708721 ≈ highlight_green%2846%29 mph