Question

Из посёлка выехал велосипедист со скоростью 15 км/ч.Через 3 часа вслед за ним выехал мотоциклист, скорость которого в 4 раза больше скорости велосипедиста. Через какое время мотоциклист догонит велосипедиста?

Answer 1

До выезда мотоциклиста велосипедист успеет проехать 15*3 = 45 км.

Скорость мотоциклиста равна 15*4 =60 км/ч, она больше скорости велосипедиста на 60-15 = 45 км/ч. Как раз столько нужно нагнать мотоциклисту. Значит он догонит велосипедиста за 1 час 45 км/45км/ч =1 час.

Answer 2

Через 1 час мотоциклист догонит велосипедиста

Answer 3

Problem Analysis

We are given that a cyclist leaves a village at a speed of 15 km/h. After 3 hours, a motorcyclist leaves the village and their speed is 4 times greater than the speed of the cyclist. We need to determine how long it will take for the motorcyclist to catch up to the cyclist.

Solution

Let's assume that the time it takes for the motorcyclist to catch up to the cyclist is t hours.

Since the cyclist has been traveling for 3 hours before the motorcyclist starts, the distance traveled by the cyclist is given by:

distance_cyclist = speed_cyclist * time_cyclist = 15 km/h * 3 hours = 45 km The speed of the motorcyclist is 4 times greater than the speed of the cyclist, so the speed of the motorcyclist is:

speed_motorcyclist = 4 * speed_cyclist = 4 * 15 km/h = 60 km/h

The distance traveled by the motorcyclist is given by:

distance_motorcyclist = speed_motorcyclist * time_motorcyclist = 60 km/h * t hours

Since the motorcyclist catches up to the cyclist, the distance traveled by the motorcyclist is equal to the distance traveled by the cyclist:

distance_motorcyclist = distance_cyclist

Substituting the values, we have:

60 km/h * t hours = 45 km

Simplifying the equation, we can solve for t:

t = 45 km / 60 km/h = 0.75 hours

Therefore, the motorcyclist will catch up to the cyclist after 0.75 hours, or 45 minutes.

Answer

The motorcyclist will catch up to the cyclist after 0.75 hours or 45 minutes.