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11 Jun 2018, 22:49
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:38) correct
37%
(02:31)
wrong
based on 201
sessions
History
Date
Time
Result
Not Attempted Yet
The distance between Mercury and Earth changes due to the orbits of the planets. When Mercury is at its closest point to Earth, it is 48 million miles away. When Mercury is at its furthest point from Earth, it is 138 million miles away. For a science project, Ruby calculates the maximum and minimum amount of time it would take to travel from Earth to Mercury in a spacecraft traveling 55 miles per hour. Approximately what are the times, in days?
(A) 3,636 and 10,454
(B) 14,545 and 41,818
(C) 36,364 and 104,545
(D) 87,272 and 250,909
(E) 872,727 and 2,509,091
(A) 3,636 and 10,454
(B) 14,545 and 41,818
(C) 36,364 and 104,545
(D) 87,272 and 250,909
(E) 872,727 and 2,509,091
11 Jun 2018, 23:14
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Solution
Given:
- • When Mercury is at its closest point to Earth, the distance between them is 48 million miles
• When Mercury is at its furthest point from Earth, the distance between them is 138 million miles
• The speed of spacecraft is 55 miles per hour
To find:
- • The maximum and minimum time the spacecraft will take to travel from Earth to Mercury
Approach and Working:
Closest distance = 48 million miles = 48000000 miles
- • Therefore, the minimum time required = \(\frac{48000000}{55} hours = 872727 hours = \frac{872727}{24} days = 36363 days\)
Furthest distance = 138 million miles = 138000000 miles
- • Therefore, the maximum time required = \(\frac{138000000}{55} hours = 2509090 hours = \frac{2509090}{24} days = 104545 days\)
Hence, the correct answer is option C.
Answer: C
12 Jun 2018, 19:36
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Bunuel
These answer choices are really far apart. Estimate.
Shortest distance is 48 million miles
48 million = \(48 * 10^6\) miles
Greatest distance is 138 million miles
138 million = \(138 * 10^6\) miles
(1) Find miles per day
Calculating (55 mph * 24 hours) is neither quick nor necessary. Change 55 mph, thus:
55 mph \(\approx\) 50 mph
Approximate miles per day?
\(\frac{50miles}{1hour}*\frac{24hours}{1 day}\approx\frac{1,200miles}{1day}\)
\(1,200 = 12 * 10^2\) miles per day
(2) Find time needed for shortest distance
\(t=\frac{D}{r}\)
\(t_1=\frac{48*10^6}{12*10^2}=\)
\((4*10^{(6-2)})=(4*10^4)=40,000\) days
Look at answer choices for something close
Answer C, time for shortest distance: 36,364
-- 40,000 is close to 36,364
-- Both are in the ten thousands
-- No other answer's time for shortest distance is close to 40,000
Answer C
(3) Doubt? Find the time needed to cover the greatest distance
Greatest distance: \(138 * 10^6\) miles
Adjust \(138\) to a multiple of \(12\)
\(138\approx132\)
Time needed for greatest distance?
\(t_2=(\frac{132*10^6}{12*10^2})=\)
\((11*10^{(6-2)})=(11*10^4)=110,000\) days
Compare these answers to answer choices.
Time in days, fewest and most:
These) 40,000 and 110,000
Ans. C) 36,364 and 104,545
The other answers are not close at all.
Answer C
