# 4. Variant 1

The train was moving from point A to point B at a constant speed. Halfway through the journey, a breakdown occurred, and the train stopped for 15 minutes. After that, the driver had to increase the train's speed by 4 times to arrive at point B on schedule. How many minutes does the train travel from point A to point B according to the schedule?
Answer: 40.

Solution. Let's represent the train's path as a segment divided into 8 parts. Denote the intervals it travels in equal time with arcs.

![](https://cdn.mathpix.com/cropped/2024_05_06_cd3ddbbeed702155f0e9g-4.jpg?height=163&width=680&top_left_y=1721&top_left_x=709)

Since the train stopped for 15 minutes, its travel time with the breakdown is 15 minutes less than the scheduled time. This time difference corresponds to \(4-1=3\) intervals. Therefore, one interval is \(15 \div 3 = 5\) minutes, and the entire journey takes \(5 \times 8 = 40\) minutes.

## Variant 2

A train was traveling from point A to point B at a constant speed. Halfway through the journey, a breakdown occurred, and the train stopped for 12 minutes. After that, the driver had to increase the train's speed by 5 times to arrive at point B on schedule. How many minutes does the train travel from point A to point B according to the schedule?

Answer: 30.

## Variant 3

A train was traveling from point A to point B at a constant speed. Halfway through the journey, a breakdown occurred, and the train stopped for 14 minutes. After that, the driver had to increase the train's speed by 3 times to arrive at point B on schedule. How many minutes does the train travel from point A to point B according to the schedule?

Answer: 42.

## Variant 4

A train was traveling from point A to point B at a constant speed. Halfway through the journey, a breakdown occurred, and the train stopped for 20 minutes. After that, the driver had to increase the train's speed by 6 times to arrive at point B on schedule. How many minutes does the train travel from point A to point B according to the schedule?

Answer: 48.

## Variant 5

A train was traveling from point A to point B at a constant speed. Halfway through the journey, a breakdown occurred, and the train stopped for 21 minutes. After that, the driver had to increase the train's speed by 4 times to arrive at point B on schedule. How many minutes does the train travel from point A to point B according to the schedule?

Answer: 56.