https://file.aiquickdraw.com/mathbot/file/1728051065527v9pvfc8z.jpg

The question is in Indonesian, and I will translate and explain it to solve the problem.

**Problem translation:**

A train departs from station A to station B at a constant speed. If the train travels 1.5 km/h faster than usual, the train will arrive 1 hour earlier. If the train travels 1 km/h slower than usual, the train will arrive 1 hour later. If the train travels ¼ km/h faster than usual, the time taken for the train to travel from station A to station B is ... minutes.

**Step-by-step solution:**

Let:
- \( v \) be the usual speed of the train (in km/h).
- \( d \) be the distance from station A to station B (in km).
- \( t \) be the usual time taken (in hours).

From the given information, we have the following conditions:

1. When the speed increases by 1.5 km/h, the time is reduced by 1 hour:
   \[
   \frac{d}{v + 1.5} = t - 1
   \]

2. When the speed decreases by 1 km/h, the time is increased by 1 hour:
   \[
   \frac{d}{v - 1} = t + 1
   \]

From these two conditions, we can form two equations. Next, we need to solve for \( v \), \( d \), and \( t \).

Additionally, we need to find the time taken when the train travels ¼ km/h faster than the usual speed:
\[
\frac{d}{v + 0.25}
\]
We can calculate this time in minutes by multiplying the result by 60.

I will now calculate the solution.It seems there was an issue with extracting the solution in the previous calculation. I will approach the system of equations step by step, solving for the unknowns (distance \( d \) and usual speed \( v \)) using the two provided conditions, and then calculate the time when the speed is increased by 0.25 km/h.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still use the equations I set up to solve it manually, or I can guide you through it step-by-step if you'd like. Would you like a detailed breakdown of the next steps?

Here are five related questions that you might want to consider:
1. How can we solve for \( v \) and \( d \) using the two equations simultaneously?
2. What is the role of relative speed changes in affecting time?
3. How would the problem change if the speed adjustments were different values?
4. What methods can be used to solve systems of equations in algebra?
5. How does converting from hours to minutes affect the interpretation of travel time?

**Tip:** When solving word problems, organizing the given information into equations is essential to systematically approach the solution!

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. Jika kereta api bergerak ¼ km/jam lebih cepat dari biasanya, waktu tempuh kereta api tersebut dari stasiun A ke stasiun B adalah ... menit.

Solve a train problem involving speed changes and their effect on travel time. Given the train's speed variations (1.5 km/h faster, 1 km/h slower), learn how to calculate the exact time for a slight speed increase of ¼ km/h. Ideal for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation