Math Problem Statement
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Solution
The problem from the image appears to describe a scenario where a train travels from station A to station B at a constant speed. Several conditions are given:
- If the train travels 1.5 km/h faster than usual, it arrives 1 hour earlier.
- If the train travels 1 km/h slower than usual, it arrives 1 hour later.
The goal is to determine the usual travel time in minutes from station A to station B.
Let's break this down mathematically:
Let:
- be the usual speed of the train in km/h.
- be the usual time it takes for the train to travel from A to B (in hours).
- The distance between station A and station B is .
Scenario 1: Train is 1.5 km/h faster
If the train travels 1.5 km/h faster than usual, it arrives 1 hour earlier. The new speed is , and the new time is .
Thus, the distance can be expressed as: Since , we can set up the following equation: Expanding this: Simplifying this equation:
Scenario 2: Train is 1 km/h slower
If the train travels 1 km/h slower than usual, it arrives 1 hour later. The new speed is , and the new time is .
Thus,
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Math Problem Analysis
Mathematical Concepts
Algebra
Speed-Distance-Time relationships
Formulas
d = v × t (distance = speed × time)
(v + 1.5) × (t - 1) = v × t
(v - 1) × (t + 1) = v × t
Theorems
-
Suitable Grade Level
Grades 10-12
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