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29 Jul 2024, 05:03
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Jerry starts running from the house to the barn, which is 150 meters away, at a constant speed of 2 meters per second. After 10 seconds, Tom starts running from the barn to the house at a constant speed of 3 meters per second. What will be Jerry's distance from their meeting point when Tom reaches the house?
A. 24 meters
B. 30 meters
C. 40 meters
D. 48 meters
E. 78 meters
A. 24 meters
B. 30 meters
C. 40 meters
D. 48 meters
E. 78 meters
29 Jul 2024, 05:03
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Official Solution:
Jerry starts running from the house to the barn, which is 150 meters away, at a constant speed of 2 meters per second. After 10 seconds, Tom starts running from the barn to the house at a constant speed of 3 meters per second. What will be Jerry's distance from their meeting point when Tom reaches the house?
A. 24 meters
B. 30 meters
C. 40 meters
D. 48 meters
E. 78 meters
In the initial 10 seconds, Jerry would cover 10 seconds * 2 meters per second = 20 meters. Thus, by the time Tom starts running, the distance between them would be 150 meters - 20 meters = 130 meters. Their combined speed is 2 meters per second + 3 meters per second = 5 meters per second, so they would cover that distance in 130 meters / 5 meters per second = 26 seconds. In these 26 seconds, Jerry would cover an additional 26 seconds * 2 meters per second = 52 meters. Therefore, Jerry's total distance covered to the meeting point from the house would be 52 meters + 20 meters = 72 meters.
Hence, Tom needs to cover those 72 meters to reach the house. Since the ratio of their speeds is 3 to 2, the distances they cover in the same time would be in the same ratio. Thus, in the time Tom would need to cover 72 meters, Jerry would cover 48 meters (since \(\frac{72}{d} = \frac{3}{2}\), solving for \(d\) yields \(d = 48\)).
Answer: D
Jerry starts running from the house to the barn, which is 150 meters away, at a constant speed of 2 meters per second. After 10 seconds, Tom starts running from the barn to the house at a constant speed of 3 meters per second. What will be Jerry's distance from their meeting point when Tom reaches the house?
A. 24 meters
B. 30 meters
C. 40 meters
D. 48 meters
E. 78 meters
In the initial 10 seconds, Jerry would cover 10 seconds * 2 meters per second = 20 meters. Thus, by the time Tom starts running, the distance between them would be 150 meters - 20 meters = 130 meters. Their combined speed is 2 meters per second + 3 meters per second = 5 meters per second, so they would cover that distance in 130 meters / 5 meters per second = 26 seconds. In these 26 seconds, Jerry would cover an additional 26 seconds * 2 meters per second = 52 meters. Therefore, Jerry's total distance covered to the meeting point from the house would be 52 meters + 20 meters = 72 meters.
Hence, Tom needs to cover those 72 meters to reach the house. Since the ratio of their speeds is 3 to 2, the distances they cover in the same time would be in the same ratio. Thus, in the time Tom would need to cover 72 meters, Jerry would cover 48 meters (since \(\frac{72}{d} = \frac{3}{2}\), solving for \(d\) yields \(d = 48\)).
Answer: D
12 Oct 2024, 18:44
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KarishmaB
I'm not following this question.
Jenny and Toms relative speed:
2(x+10) + 3x = 150
x = 26
In 36 seconds they will meet. So meeting point is 72 meters. 72/3 = 24 seconds. Tom has to run for 26 seconds to reach the house. Jenny would need to run 26 seconds as well.
26 * 2 = 52 meters.
Where am I making a mistake?
I'm not following this question.
Jenny and Toms relative speed:
2(x+10) + 3x = 150
x = 26
In 36 seconds they will meet. So meeting point is 72 meters. 72/3 = 24 seconds. Tom has to run for 26 seconds to reach the house. Jenny would need to run 26 seconds as well.
26 * 2 = 52 meters.
Where am I making a mistake?
