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19 Feb 2022, 03:54
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C
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In a 1000-mile, race Flash gives Superman a head start of 40 miles and beats him by 19 milliseconds. If, in a 1000-mile race, Flash gives Superman a head start of 30 milliseconds then Superman beats Flash by 40 miles. What is the ratio of speed of Flash to that of Superman ?
A. 4:5
B. 5:6
C. 6:5
D. 5:4
E. 4:3
Are You Up For the Challenge: 700 Level Questions
A. 4:5
B. 5:6
C. 6:5
D. 5:4
E. 4:3
Are You Up For the Challenge: 700 Level Questions
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Flash vs. Superman.gif
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20 Feb 2022, 11:25
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Bunuel
Breaking Down the Info:
Let the speed of Flash and Superman be \(v_f\) and \(v_s\), respectively.
For the first race, Superman took 19 ms longer, so we can translate that to \(t_f = t_s - 19\). Flash ran 1000 miles while Superman ran only 960 miles, so we have \(\frac{1000}{v_f} = \frac{960}{v_s} + 19\).
For the second sentence, we would have \(t_f = t_s - 30\) (note these times are different from before), but Superman ran the full 1000 miles while Flash only ran 960 miles. Then we have \(\frac{960}{v_f} = \frac{1000}{v_s} + 30\).
Now to find the ratio, we would like to get rid of the constant term in each equation. Multiply the first equation by 30, the second equation by 19, then subtract in order to eliminate the constant.
We would get: \(\frac{1000*30}{v_f} - \frac{960*19}{v_f} = \frac{960*30}{v_s} - \frac{1000*19}{v_s}\)
\(\frac{11760}{v_f} = \frac{9800}{v_s}\)
\(\frac{v_f}{v_s} = \frac{11760}{9800} = \frac{6}{5}\)
Answer: C
General Discussion
13 Mar 2025, 23:25
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Thank you for the explanation...i approached the problem same way till tf=ts-19 my interpretation is same...but unable to see why
[ltr]1000/vf=960/vs+19? According to my understanding it should be 1000/vf=960/vs-19....similarly in case-2, equation is coming 960/vf=1000/vx-30.(Since tf=ts-30 as you mentioned in the solution.) Please explain where I am faltering.[/ltr]
[ltr]1000/vf=960/vs+19? According to my understanding it should be 1000/vf=960/vs-19....similarly in case-2, equation is coming 960/vf=1000/vx-30.(Since tf=ts-30 as you mentioned in the solution.) Please explain where I am faltering.[/ltr]
JerryAtDreamScore
