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In an \(x\)-meter race competition, Tom gives Jerry a 240-meters head start. If Tom runs \(\frac{13}{5}\) times as fast as Jerry and if the race ends in a tie, what is the value of \(x\)?
A. 330 meters
B. 390 meters
C. 600 meters
D. 720 meters
E. 730 meters
A. 330 meters
B. 390 meters
C. 600 meters
D. 720 meters
E. 730 meters
03 Mar 2024, 02:58
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Official Solution:
In an \(x\)-meter race competition, Tom gives Jerry a 240-meters head start. If Tom runs \(\frac{13}{5}\) times as fast as Jerry and if the race ends in a tie, what is the value of \(x\)?
A. 330 meters
B. 390 meters
C. 600 meters
D. 720 meters
E. 730 meters
The main idea in this question is that since they start simultaneously and the race ends in a tie, they run for the same amount of time. Tom runs \(x\) meters, while Jerry runs \(x - 240\) meters. Now, we equate the times: \(time = \frac{distance}{rate} = \frac{x}{(\frac{13}{5}*r)} = \frac{x - 240}{r}\), where \(r\) is the rate of Jerry. When we cancel out \(r\), we get \(\frac{x}{(\frac{13}{5})} = x - 240\), which simplifies to \(5x = 13x - 240*13\). Finally, this gives us \(x = 390\) meters.
We can also plug-in answer options. If we plug B, it would mean that Tom covered 390 meters and Jerry covered 390 - 240 = 150 meters. Since they run for the same amount of time, the ratio of distance covered should match the ratio of their rates. This means that 390/150 should equal 13/5, which it does. Thus, B is the correct answer.
Answer: B
In an \(x\)-meter race competition, Tom gives Jerry a 240-meters head start. If Tom runs \(\frac{13}{5}\) times as fast as Jerry and if the race ends in a tie, what is the value of \(x\)?
A. 330 meters
B. 390 meters
C. 600 meters
D. 720 meters
E. 730 meters
The main idea in this question is that since they start simultaneously and the race ends in a tie, they run for the same amount of time. Tom runs \(x\) meters, while Jerry runs \(x - 240\) meters. Now, we equate the times: \(time = \frac{distance}{rate} = \frac{x}{(\frac{13}{5}*r)} = \frac{x - 240}{r}\), where \(r\) is the rate of Jerry. When we cancel out \(r\), we get \(\frac{x}{(\frac{13}{5})} = x - 240\), which simplifies to \(5x = 13x - 240*13\). Finally, this gives us \(x = 390\) meters.
We can also plug-in answer options. If we plug B, it would mean that Tom covered 390 meters and Jerry covered 390 - 240 = 150 meters. Since they run for the same amount of time, the ratio of distance covered should match the ratio of their rates. This means that 390/150 should equal 13/5, which it does. Thus, B is the correct answer.
Answer: B
05 Feb 2025, 09:56
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I like the solution - it’s helpful.
