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25 Sep 2025, 06:47
Kudos
Bookmarks
R: 21
S: 10
At a mountain observatory, astronomers set exposure times for two types of targets. Each faint target requires R seconds per image, and each bright target requires a shorter exposure of S seconds per image. On Night 1, the team captured 35 images using a total of 625 seconds. On Night 2, they captured 140 images using a total of 1730 seconds. On both nights, both faint and bright targets were captured.
Select for R and S values for R and S that are jointly consistent with the information provided. Make only two selections, one in each column.
Select for R and S values for R and S that are jointly consistent with the information provided. Make only two selections, one in each column.
| R | S | |
| 10 | ||
| 12 | ||
| 14 | ||
| 15 | ||
| 19 | ||
| 21 |
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Official Answer
R: 21
S: 10
25 Sep 2025, 06:47
Kudos
Bookmarks
Official Solution:
Night 1 average = 625/35 ≈ 17.9
Night 2 average = 1730/140 ≈ 12.4
So S must be below both averages and R must be above both. Since R > S, that narrows to R = 19 or 21, and S = 10, 12, or 14.
Night 1 equation is xR + (35 - x)S = 625, where x is the number of faint images on Night 1.
First test R = 19. Substituting gives 19x + S(35 - x) = 625. For S = 10, 12, or 14, this does not give an integer solution for x, so R cannot be 19.
Now test R = 21. Substituting gives 21x + S(35 - x) = 625.
For S = 10, this gives x = 25, which is an integer solution.
For S = 12 or 14, no integer solution exists.
Therefore the only consistent pair is R = 21 and S = 10.
Correct answer:
R "21"
S "10"
Bunuel
Night 1 average = 625/35 ≈ 17.9
Night 2 average = 1730/140 ≈ 12.4
So S must be below both averages and R must be above both. Since R > S, that narrows to R = 19 or 21, and S = 10, 12, or 14.
Night 1 equation is xR + (35 - x)S = 625, where x is the number of faint images on Night 1.
First test R = 19. Substituting gives 19x + S(35 - x) = 625. For S = 10, 12, or 14, this does not give an integer solution for x, so R cannot be 19.
Now test R = 21. Substituting gives 21x + S(35 - x) = 625.
For S = 10, this gives x = 25, which is an integer solution.
For S = 12 or 14, no integer solution exists.
Therefore the only consistent pair is R = 21 and S = 10.
Correct answer:
R "21"
S "10"
02 Nov 2025, 02:18
Kudos
Bookmarks
Hi Bunuel !
How did you assume R > S. No where in the question its mentioned that R> S . Could you please clarify? Thanks
How did you assume R > S. No where in the question its mentioned that R> S . Could you please clarify? Thanks
Bunuel
