On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The difference between their speeds, in km per hour, is
Correct Answer: 50
Solution and Explanation
To solve this problem, we need to determine the speeds of the two cars and find the difference between them. Let's denote the speed of the car starting from A as \( v_A \) km/h and the speed of the car starting from B as \( v_B \) km/h.
Case 1: Cars move towards each other
When the cars move towards each other, they cover the 350 km distance in 1 hour. Therefore,
\( v_A + v_B = 350 \).
Case 2: Cars move in the same direction towards east
When both cars move eastwards, the car from B needs to catch up 350 km ahead, and they meet in 7 hours. Therefore, the effective relative speed becomes \( v_A - v_B \). Thus,
\((v_A - v_B) \times 7 = 350\), which simplifies to \( v_A - v_B = 50 \).
Now, we have the system of linear equations:
\( v_A + v_B = 350 \)
\( v_A - v_B = 50 \)
By solving these, we add the equations:
\((v_A + v_B) + (v_A - v_B) = 350 + 50\)
\(2v_A = 400\)
\(v_A = 200\)
Substituting \( v_A = 200 \) into \( v_A + v_B = 350 \), we get:
\(200 + v_B = 350\)
\(v_B = 150\)
The difference in their speeds is \( v_A - v_B = 200 - 150 = 50 \) km/h, which fits the given range of 50,50.
Therefore, the difference between their speeds is 50 km/h.
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