Question

Путешественник, едущий из `A` в `B`, одну половину затраченного на путь времени ехал на мотоцикле, а вторую – на автобусе. Если бы он всю дорогу ехал на мотоцикле, он бы затратил в `1,5` раза меньше времени. Во сколько раз быстрее проходит путь от `A` до `B` мотоцикл, чем автобус?

Answer 1

Ответ:

В три раза

Пошаговое объяснение:

S – путь

V – скорость мотоцикла

v₁ – скорость автобуса.

Время по условию задачи: (0.5*S):V + (0.5*S):v₁

Время езды только на автобусе: S:v₁

Отношение времени 1.5

S:v₁ =1.5 * ((0.5*S):V + (0.5*S):v₁) ;

S:v₁ = 0.75*S*(1/V+1/v₁)

разделим обе части уравнения на S;

1:v₁ = 0.75*(1:V+1:v₁)

1 = 0.75*(v₁:V+1)

4/3 - 1 = v₁:V

1/3= v₁:V

V = 3v₁. - скорость мотоцикла в 3 раза быстрее скорости автобуса.

Время, затраченное на поездку только на мотоцикле было бы в 3 раза меньше

Можно было и проще, без уравнений: если половина дороги на мотоцикле в полтора раза быстрее, то и вторая половина на мотоцикле в полтора раза быстрее 1,5 + 1,5 = 3, т.е. в три раза быстрее на мотоцикле, чем на автобусе.

Answer 2

Problem Analysis

A traveler is going from point A to point B. They spend half of the total travel time on a motorcycle and the other half on a bus. If they had traveled the entire distance on a motorcycle, they would have spent 1.5 times less time. We need to determine how much faster the motorcycle is compared to the bus for the journey from A to B.

Solution

Let's assume that the total travel time from A to B is represented by the variable `T`. According to the problem, the traveler spends half of the time on a motorcycle and the other half on a bus. Therefore, the time spent on each mode of transportation is `T/2`.

If the traveler had traveled the entire distance on a motorcycle, they would have spent 1.5 times less time. This means that the time spent on a motorcycle would be `(T/2) / 1.5`.

To find out how much faster the motorcycle is compared to the bus, we need to calculate the ratio of the time spent on the bus to the time spent on the motorcycle.

Let's calculate the ratio:

Time spent on the bus: `T/2`

Time spent on the motorcycle: `(T/2) / 1.5`

Ratio of motorcycle time to bus time: `((T/2) / 1.5) / (T/2)`

Simplifying the expression:

Ratio of motorcycle time to bus time: `1 / 1.5`

Therefore, the motorcycle is 1.5 times faster than the bus for the journey from A to B.