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myuan's question:
Frank and Grace set off from A and B at the same time and traveled in the opposite direction. They meet at point C after 6 hours.
If Frank's speed is the same, Grace's speed is increased by 5 km/h, and the two of them start from A and B at the same time, then the meeting point D is 12 kilometers away from point C.
If Grace's speed is the same, Frank's speed is increased by 5 km/h, and the two of them start from A and B at the same time, then the meeting point E is 16 kilometers away from point C.
Q: Please find the distance between A and B.
未名ChatGPT:
Let Frank's speed be x km/h, and let Grace's speed be x + 5 km/h.
According to the problem,
they meet at point C after 6 hours.
Then, they travel for 6 hours in opposite directions.
Therefore, they meet at a distance of 6x + 6(x + 5) = 6(2x + 5) kilometers from A and B.
In other words, A and B are 6(2x + 5) kilometers away from C.
Therefore, when the speed of Grace is increased by 5 km/h and the two of them start from A and B at the same time,
the distance between A and B is 12 kilometers less than that of Frank's speed.
The distance between A and B is 12 + 6(2x + 5) = (3x + 36) kilometers.
When Frank's speed is increased by 5 km/h, the distance between A and B is 16 kilometers less than that of Grace's speed.
The distance between A and B is (3x + 36) - 16 = (3x + 20) kilometers.
Therefore, we have (3x + 36) = (3x + 20) + (2 × 6).
This gives us x = 8 km/h.
The distance between A and B is (3 × 8 + 20) = (44) kilometers.
Therefore, the distance between A and B is 44 kilometers.
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