Question

Дорога из города А в город В, длина которой 260 км, идёт сначала в гору, а затем под гору. На подъёме автобус ехал со скоростью 30 км/ч, а на спуске - со скоростью 50 км/ч, затратив на спуск на 2 ч больше, чем на подъём. Какое время затртил автобус на весь путь?

Answer 1

х время в пути автобуса в гору

х+2 время в пути автобуса на спуске

30х+50(х+2)=260

30х+50х+100=260

80х+100=260

80х=160

х=2 часа ехал в гору

2+2= 4 часа ехал на спуске

2+4=6 часов всё время в пути

Answer 2

Problem Analysis

We are given that a bus travels from city A to city B, a distance of 260 km. The road first goes uphill, and then downhill. The bus travels at a speed of 30 km/h uphill and 50 km/h downhill. The time spent on the downhill portion is 2 hours more than the time spent on the uphill portion. We need to find the total time spent by the bus on the entire journey.

Solution

Let's assume that the time spent on the uphill portion is t hours. Since the speed uphill is 30 km/h, the distance covered uphill is 30t km.

According to the given information, the time spent on the downhill portion is 2 hours more than the time spent on the uphill portion. So, the time spent on the downhill portion is t + 2 hours. Since the speed downhill is 50 km/h, the distance covered downhill is 50(t + 2) km.

The total distance covered by the bus is the sum of the distances covered uphill and downhill, which is 30t + 50(t + 2) km.

We know that the total distance covered is 260 km. So, we can set up the following equation:

30t + 50(t + 2) = 260

Simplifying the equation:

30t + 50t + 100 = 260

80t + 100 = 260

80t = 160

t = 2

Therefore, the time spent on the uphill portion is 2 hours.

To find the total time spent by the bus on the entire journey, we need to add the time spent on the uphill and downhill portions:

Total time = time spent uphill + time spent downhill = 2 hours + (2 + 2) hours = 2 hours + 4 hours = 6 hours

Therefore, the bus spent 6