SOLUTION: In a Grand Prix automobile race with five different race cars, Rapid Ravi averaged 90 mi/hr for the first half of the course and 110 mi/hr for the second half of the course. Steady

Algebra ->  Rate-of-work-word-problems -> SOLUTION: In a Grand Prix automobile race with five different race cars, Rapid Ravi averaged 90 mi/hr for the first half of the course and 110 mi/hr for the second half of the course. Steady      Log On


   

Question 1106772: In a Grand Prix automobile race with five different race cars, Rapid Ravi averaged 90 mi/hr for the first half of the course and 110 mi/hr for the second half of the course. Steady Spencer maintained a constant speed of 100 mi/hr throughout the race. They were the only two cars to complete the race. Who won the race? How much did the winner win by?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
In a Grand Prix automobile race with five different race cars,
Rapid Ravi averaged 90 mi/hr for the first half of the course and 110 mi/hr for the second half of the course.
Steady Spencer maintained a constant speed of 100 mi/hr throughout the race.
They were the only two cars to complete the race.
Who won the race? How much did the winner win by?
:
let d = the distance of half the race
Find the total time of R, (time = dist/speed)
{{d/90}}} + d%2F110
Common denominator is 990
%2811d+%2B+9d%29%2F990 = %2820d%29%2F990
simplifies to
%282d%29%2F99 = the time of R
:
Find the time of S
%282d%29%2F100 is S's time and so he wins the race.
:
"How much did the winner win by?:
they don't give the length of the race track, no. of laps, etc
Assuming they use the 2 hr rule
S travels 2 * 100 = 200 mi
R travels 2 * 99 = 198 mi
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winner wins by: 2 mi