jamifahad wrote:
Three runners A, B and C run a race, with runner A finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?
A. 36m
B. 48m
C. 60m
D. 72m
E. 84m
Part 1:
A finishing 12m ahead of runner B and 18m ahead of runner C.At this point:
Since B is 12 meters behind A, B must travel 12 more meters to finish the race.
Since C is 18 meters behind A, C must travel 18 more meters to finish the race.
Part 2:
B finishes 8m ahead of runner CAt this point:
Since B finishes the race, B just traveled the remaining 12 meters.
Whereas the remaining distance for C in Part 1 was 18 meters, the remaining distance for C in Part 2 is 8 meters.
Implication:
C just traveled 10 meters.
Since B travels 12 meters in the time it takes C to travel 10 meters, the rate ratio for B to C \(= \frac{12}{10} = \frac{6}{5}\).
We can PLUG IN THE ANSWERS, which represent the total distance.
When the correct answer is plugged in, Part 1 will yield for B and C a rate ratio of \(\frac{6}{5}\).
In Part 1, B finishes 12 meters behind A, while C finishes 18 meters behind A.
D: 72
Part 1 --> A=72 meters, B=72-12=60 meters, C=72-18=54 meters
Rate ratio for \(\frac{B}{C} = \frac{60}{54} = \frac{10}{9}\)
Eliminate D.
B: 48
Part 1 --> A=48 meters, B=48-12=36 meters, C=48-18=30 meters
Rate ratio for \(\frac{B}{C }= \frac{36}{30} = \frac{6}{5}\)
Success!
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