Question

От населенного пункта до ближайшей станции туристы едут на автобусе. Если автобус будет ехать со скоростью 60км/ч, то они прибудут на станцию на 20 мин. раньше. Если автобус будет ехать со скоростью 50 км/ч, то они прибудут на станцию на 12 мин позже. Каково расстояния от населенного пункта до ближайшей станции?

Answer 1

Пусть х-среднее время

V=60км/ч, тогда t=х-20мин=х-1/3час

V=50км/ч, тогда t=х+12мин=х+1/5час

Так как расстояние одно и тоже, то составим уравнение:

60×(х-1/3)=50×(х+1/5)

60х-20=50х+10

10х=30

х=3час -среднее время. Подставим:

V=60км/ч, тогда t=х-20мин=х-1/3час=3-1/3

расстояние=скорость×время

s=60×(3-1/3)=180-60×1/3=180-20=160км - расстояние

 

Answer 2

Problem Analysis

We are given that tourists travel from a settlement to the nearest station by bus. If the bus travels at a speed of 60 km/h, they arrive at the station 20 minutes early. If the bus travels at a speed of 50 km/h, they arrive at the station 12 minutes late. We need to find the distance from the settlement to the nearest station.

Solution

Let's assume that the distance from the settlement to the nearest station is d km.

If the bus travels at a speed of 60 km/h, the time taken to cover the distance d is given by:

d / 60 = t - 20/60

where t is the time taken in hours.

If the bus travels at a speed of 50 km/h, the time taken to cover the distance d is given by:

d / 50 = t + 12/60

We can solve these two equations to find the value of d.

Calculation

Let's solve the equations:

d / 60 = t - 20/60

d / 50 = t + 12/60

We can rewrite these equations as:

d = 60(t - 20/60)

d = 50(t + 12/60)

Setting the two equations equal to each other:

60(t - 20/60) = 50(t + 12/60)

Simplifying the equation:

60t - 20 = 50t + 12

10t = 32

t = 3.2

Substituting the value of t back into one of the equations:

d = 60(3.2 - 20/60)

d = 60(3.2 - 1/3)

d = 60(9.6/3 - 1/3)

d = 60(8.6/3)

d = 60(2.8667)

d ≈ 172 km

Answer

The distance from the settlement to the nearest station is approximately 172 km.