Question

Из города выехал велосипедист. Через 40мин вслед за ним выехал мотоциклист, скорость которого в два раза больше, чем у велосипедиста. Сколько времени потребуется мотоциклисту, чтобы догнать велосипедиста? Подскажите пожалуйста решение.

Answer 1

Дано V2=2*V1 t1=40 мин   t2- ?

L=V1*t1 - расстояние которое проехал велосипедист

t2=L/V=L/(V2-V1)=V1*t1/(2*V1-V1)=t1=40 мин

Ответ t2=40 мин

Answer 2

Problem Analysis

We are given that a cyclist leaves a city, and after 40 minutes, a motorcyclist leaves the same city. The motorcyclist's speed is twice that of the cyclist. We need to determine how much time it will take for the motorcyclist to catch up to the cyclist.

Solution

Let's assume the speed of the cyclist is x units (e.g., km/h), and the speed of the motorcyclist is 2x units.

We know that the distance covered by the cyclist in 40 minutes is equal to the distance covered by the motorcyclist when they catch up.

To find the time it takes for the motorcyclist to catch up to the cyclist, we can set up the following equation:

Distance covered by the cyclist = Distance covered by the motorcyclist

The distance covered by the cyclist can be calculated by multiplying the speed of the cyclist by the time taken:

Distance covered by the cyclist = x * (40/60) = (2/3)x

The distance covered by the motorcyclist can be calculated by multiplying the speed of the motorcyclist by the time taken:

Distance covered by the motorcyclist = 2x * t

where t is the time taken for the motorcyclist to catch up to the cyclist.

Setting the two distances equal to each other, we have:

(2/3)x = 2x * t

Simplifying the equation, we get:

(2/3) = 2t

Solving for t, we find:

t = (2/3) / 2 = 1/3

Therefore, it will take the motorcyclist 1/3 of an hour to catch up to the cyclist.

Answer

The motorcyclist will take 1/3 of an hour to catch up to the cyclist.

Note: The solution assumes constant speeds for both the cyclist and the motorcyclist throughout the duration of the problem.