Question

Из поселка выехал велосипедист со скоростью 15 км/ч через 3 часа вслед за ним выехал мотоциклист скорость в 4 раза больше велосипедиста,через какое время мотоциклист догонит велосипедиста

Answer 1

1) 15*4=60 км/ч - скорость мот.
2) 15*3=45 км - расстояние между вел. и мот. перед выездом мотоциклиста.
3) 60-15=45 км/ч - скорость, с которой сокращается расстояние между мот. и вел.
4) 45 км:45 км/ч = 1 час
Ответ: 1.

Answer 2

Problem Analysis

We are given that a cyclist is traveling at a speed of 15 km/h, and after 3 hours, a motorcyclist starts following the cyclist with a speed 4 times greater than the cyclist's speed. We need to determine how long it will take for the motorcyclist to catch up to the cyclist.

Solution

Let's calculate the distance traveled by the cyclist in 3 hours and the relative speed between the motorcyclist and the cyclist.

The distance traveled by the cyclist in 3 hours can be calculated using the formula:

Distance = Speed × Time

Substituting the given values, we have:

Distance = 15 km/h × 3 hours

Now, let's calculate the relative speed between the motorcyclist and the cyclist. Since the motorcyclist's speed is 4 times greater than the cyclist's speed, the relative speed can be calculated as:

Relative Speed = Motorcyclist's Speed - Cyclist's Speed

Substituting the given values, we have:

Relative Speed = (4 × 15 km/h) - 15 km/h

Now, we can calculate the time it will take for the motorcyclist to catch up to the cyclist using the formula:

Time = Distance / Relative Speed

Substituting the calculated values, we have:

Time = (15 km/h × 3 hours) / [(4 × 15 km/h) - 15 km/h]

Let's calculate the time.

Calculation

Distance traveled by the cyclist in 3 hours: Distance = 15 km/h × 3 hours = 45 km

Relative speed between the motorcyclist and the cyclist: Relative Speed = (4 × 15 km/h) - 15 km/h = 45 km/h

Time it will take for the motorcyclist to catch up to the cyclist: Time = 45 km / 45 km/h = 1 hour

Answer

The motorcyclist will catch up to the cyclist in 1 hour.

Explanation

The cyclist travels at a speed of 15 km/h for 3 hours, covering a distance of 45 km. The motorcyclist, with a speed 4 times greater than the cyclist's speed, has a relative speed of 45 km/h. Therefore, it will take the motorcyclist 1 hour to cover the same distance and catch up to the cyclist.