Math Problem Statement
Steven stands on a bridge AB. His distance from A is 7 16 of the distance AB. A train is coming toward A at a speed of 80 km/h. Steven has two choices. He can either run toward A and he will meet the train at A, or he can run toward B at the same speed then the train will catch up him at B. Find his speed in km/h.
Solution
To solve this problem, let the total distance between points and be . Given that Steven is standing of the distance from , his distance from point is , and his distance from point is .
Let Steven's speed be km/h. The speed of the train is given as 80 km/h.
Case 1: Running toward
When Steven runs toward , the distance he needs to cover is . Since he and the train meet at , the time taken for both will be the same.
The time taken by Steven to reach is:
The time taken by the train to reach is:
Since , we have:
Canceling out from both sides:
Solving for :
Case 2: Running toward
When Steven runs toward , the distance he needs to cover is . The train will also cover this same distance by the time it catches up to him.
The time taken by Steven to reach is:
The time taken by the train to reach is:
Since , we have:
Canceling out from both sides:
Solving for :
Conclusion
The speed of Steven in both cases is and . Therefore, the answer is 35 km/h.
Would you like more details or have any questions?
Here are some related problems:
- If the train's speed were doubled, what would be Steven's new running speed?
- How would the problem change if Steven started at the midpoint of the bridge?
- What would happen if Steven could only run at half his current speed?
- How long would it take the train to reach Steven if he remained stationary?
- If Steven had a head start, how much time would he need to reach safety at point A?
Tip: When solving time-speed problems, always relate the distance covered to the time taken, as time remains constant in uniform motion scenarios.
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Math Problem Analysis
Mathematical Concepts
Speed, Distance, Time Problems
Formulas
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Theorems
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Suitable Grade Level
High School
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