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22 Dec 2025, 12:14
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Alpha - 32 Beta - 40
Not sure how to solve this besides picking numbers and it took me a while. If anyone has a faster way, please reply.
Since the distances of each are the same, we can set up the equation:
A*k = B*(k-2.5), where A and B are the rates of each ship.
Expanding:
Ak=Bk-2.5B
Pick: 40 for Alpha. That will give 10 for k. 400=10b-2.5b, or 400 = 7.5b.
Begin long division (4,000/75) and see that 75 goes into 400 5 times, we can stop because it will not be 50 so we can stop to save time.
Pick: 32 for Alpha. That will give 12.5 for k. Substituting into our eqution:
400=12.5b-2.5b or b =40.
A - 32, B - 40.
Not sure how to solve this besides picking numbers and it took me a while. If anyone has a faster way, please reply.
Since the distances of each are the same, we can set up the equation:
A*k = B*(k-2.5), where A and B are the rates of each ship.
Expanding:
Ak=Bk-2.5B
Pick: 40 for Alpha. That will give 10 for k. 400=10b-2.5b, or 400 = 7.5b.
Begin long division (4,000/75) and see that 75 goes into 400 5 times, we can stop because it will not be 50 so we can stop to save time.
Pick: 32 for Alpha. That will give 12.5 for k. Substituting into our eqution:
400=12.5b-2.5b or b =40.
A - 32, B - 40.
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22 Dec 2025, 12:29
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Solution:
Average speed = Total Distance/Total time
By looking at the options, the only information that falls jointly consistent for Ship Alpha is 32, and Ship Beta is 40.
Ship Alpha's average speed = 400/32 = k, where the value for K is 12.5. So, let's apply it to the equation Ship Beta's average speed = 400/(12.5-2.5)=40.
Average speed = Total Distance/Total time
By looking at the options, the only information that falls jointly consistent for Ship Alpha is 32, and Ship Beta is 40.
Ship Alpha's average speed = 400/32 = k, where the value for K is 12.5. So, let's apply it to the equation Ship Beta's average speed = 400/(12.5-2.5)=40.
Bunuel
22 Dec 2025, 12:38
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Bunuel
Let A = rate of Ship A and B = rate of Ship B.
\(k=\frac{400}{A}\)
\(k=\frac{400+2.5B}{B}=\frac{400}{B}+2.5\)
We are looking for values such that:
\(\frac{400}{A}=\frac{400}{B}+2.5\)
To make our life easier, let's divide 400 by all the answer choices and then identify which two numbers are 2.5 apart.
\(\frac{400}{25}=16\)
\(\frac{400}{32}=\frac{25}{2}=\frac{50}{4}\)
\(\frac{400}{40}=10\)
\(\frac{400}{50}=8\)
\(\frac{400}{64}=\frac{25}{4}\)
\(\frac{400}{80}=5\)
For more simplicity, let's convert 2.5 into fractions. \(2.5=\frac{5}{2}=\frac{10}{4}\)
After testing to see which numbers are 2.5 apart, we see that \(10=\frac{40}{4}+\frac{10}{4}=\frac{50}{4}\). So 32 and 40 are our answers. We know that Ship Beta is faster, so it's speed is 40 and Ship A is then 32.
