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Updated on: 02 Oct 2023, 14:11
Originally posted by Sajjad1994 on 29 Oct 2020, 00:04.
Last edited by BottomJee on 02 Oct 2023, 14:11, edited 2 times in total.
Last edited by BottomJee on 02 Oct 2023, 14:11, edited 2 times in total.
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Car A: 35
Car B: 35
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
79% (01:51) correct
21%
(02:50)
wrong
based on 453
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Two cars, Car A and Car B, are driving toward each other along the same road at constant speeds. They start 210 miles apart, and in 3 hours they will meet. In the table, identify a speed, in miles per hour, for Car A and a speed, in miles per hour, for Car B that together are consistent with the given information. Make only one selection in each column.
| Car A | Car B | ---------- |
| 20 | ||
| 30 | ||
| 35 | ||
| 45 | ||
| 55 | ||
| 60 |
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Official Answer
Car A: 35
Car B: 35
31 Oct 2020, 06:40
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When 2 objects are moving in the same direction at the same time, their speeds are subtracted.
When 2 objects are moving in the opposite direction at the same time, their speeds are added.
Since the cars are driving towards each other, the relative speed is the sum of the speeds.
They are 210 miles apart and will meet in 3 hours. Therefore RS = D/T = 210/3 = 70
Sum of the speeds is 70 miles/hour and from the table the only possibility to give a sum of 70 is that both travel at the same speed of 35 miles / hour.
Arun Kumar
When 2 objects are moving in the opposite direction at the same time, their speeds are added.
Since the cars are driving towards each other, the relative speed is the sum of the speeds.
They are 210 miles apart and will meet in 3 hours. Therefore RS = D/T = 210/3 = 70
Sum of the speeds is 70 miles/hour and from the table the only possibility to give a sum of 70 is that both travel at the same speed of 35 miles / hour.
Arun Kumar
13 Jan 2021, 01:00
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Official Explanation
Two-Part Analysis questions may be quantitative or verbal; and the correct answers in the two columns may be independent of or dependent on each other. In this case, you have a quantitative question with answers that are dependent on each other. Let \(r_{A}\) be Car A’s speed and \(r_{B}\) be Car B’s speed, and let \(d_{A}\) be the distance that Car A will have traveled when the two cars meet, and dB be the distance that Car B will have traveled when they meet. The two distances will add up to 210 miles when the two cars meet:
\(d_{A} + d_{B} = 210 d_{B} = 210 – d_{A}\) You also know that distance equals speed times time, and since time in this case is 3 hours (the time it will take for the two cars to meet), you have: \(d_{A} = 3r_{A}\) and So, you have arrived at an expression that relates the speeds of the two cars. You cannot go further than this and calculate what the speeds are—but you also don’t have to do that. You simply have to pick two answer choices that, together, satisfy this expression. In other words, you are looking for two answer choices whose sum equals 70. Here’s a further tricky point: These two answer choices may be different from each other, but they don’t have to be. In this case, the only way two of the answer choices can add up to 70 is if they are both 35. Thus, choice (C) is the correct answer for the speed of both cars.
1.1. The correct answer is (C).
1.2. The correct answer is (C).
Two-Part Analysis questions may be quantitative or verbal; and the correct answers in the two columns may be independent of or dependent on each other. In this case, you have a quantitative question with answers that are dependent on each other. Let \(r_{A}\) be Car A’s speed and \(r_{B}\) be Car B’s speed, and let \(d_{A}\) be the distance that Car A will have traveled when the two cars meet, and dB be the distance that Car B will have traveled when they meet. The two distances will add up to 210 miles when the two cars meet:
\(d_{B}=3r_{B}\)
\(210-d_{A}=3r_{B}\)
\(210-3r_{A}=3r_{B}\)
\(3r_{B}+3r_{B}=210\)
\(r_{B}+r_{A}=70\)
\(210-d_{A}=3r_{B}\)
\(210-3r_{A}=3r_{B}\)
\(3r_{B}+3r_{B}=210\)
\(r_{B}+r_{A}=70\)
\(d_{A} + d_{B} = 210 d_{B} = 210 – d_{A}\) You also know that distance equals speed times time, and since time in this case is 3 hours (the time it will take for the two cars to meet), you have: \(d_{A} = 3r_{A}\) and So, you have arrived at an expression that relates the speeds of the two cars. You cannot go further than this and calculate what the speeds are—but you also don’t have to do that. You simply have to pick two answer choices that, together, satisfy this expression. In other words, you are looking for two answer choices whose sum equals 70. Here’s a further tricky point: These two answer choices may be different from each other, but they don’t have to be. In this case, the only way two of the answer choices can add up to 70 is if they are both 35. Thus, choice (C) is the correct answer for the speed of both cars.
1.1. The correct answer is (C).
1.2. The correct answer is (C).
