Math Problem Statement

Kerjakan soal nomor 1

Sebuah kereta api berangkat dari stasiun A ke stasiun B dengan kecepatan konstan. Jika kereta api bergerak 1,5 km/jam lebih cepat dari biasanya, kereta akan tiba 1 jam lebih awal. Jika kereta api bergerak 1 km/jam lebih lambat dari biasanya, kereta akan tiba 1 jam lebih lambat. Waktu tempuh kereta api tersebut dari stasiun A ke stasiun B adalah ... menit.

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:

  1. If the train travels 1.5 km/h faster than usual, it arrives 1 hour earlier.
  2. 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:

  • vv be the usual speed of the train in km/h.
  • tt 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 d=v×td = v \times t.

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 v+1.5v + 1.5, and the new time is t1t - 1.

Thus, the distance dd can be expressed as: d=(v+1.5)(t1)d = (v + 1.5)(t - 1) Since d=v×td = v \times t, we can set up the following equation: v×t=(v+1.5)(t1)v \times t = (v + 1.5)(t - 1) Expanding this: v×t=(v+1.5)t(v+1.5)v \times t = (v + 1.5)t - (v + 1.5) v×t=v×t+1.5tv1.5v \times t = v \times t + 1.5t - v - 1.5 Simplifying this equation: 0=1.5tv1.5(Equation 1)0 = 1.5t - v - 1.5 \quad \text{(Equation 1)}

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 v1v - 1, and the new time is t+1t + 1.

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

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Suitable Grade Level

Grades 10-12