Question

Из пункта А в пункт В автомобиль ехал по шоссе протяженностью 210 км, а возвращался назад по грунтовой дороге протяженностью 160 км , затратив на обратный путь на 1 час больше , чем на путь из А в В. С какой скоростью автомобиль двигался по грунтовой дороге , если она на 30 км в час меньше его скорости по шоссе. А.30 км/ч Б.40км/ч. В.50км/ч. Г.60км/ч

Answer 1

Скорости v; v-30
210/v+1=160/(v-30)    160/(v-30)-210/v=1
v²-30v=160v-210v+6300
v²+20v-6300=0   D=400+4*6300=25600  √D=160
v=1/2[-20+160]= 70 км/час  v=1/2[-20-160]<0

vгр=70-30=40 км/час    ответ Б)

Answer 2

Problem Analysis

We are given that a car traveled from point A to point B on a highway with a distance of 210 km. On the return journey from point B to point A, the car traveled on a dirt road with a distance of 160 km. The car took 1 hour longer to return than it took to go from point A to point B. We need to determine the speed at which the car traveled on the dirt road, given that it was 30 km/h slower than its speed on the highway.

Solution

Let's assume the speed of the car on the highway is x km/h. According to the problem, the speed of the car on the dirt road is 30 km/h slower than its speed on the highway, so the speed on the dirt road is x - 30 km/h.

To find the time it took for the car to travel from point A to point B on the highway, we can use the formula: time = distance / speed. Therefore, the time taken on the highway is 210 / x hours.

On the return journey, the car traveled on the dirt road, which is 160 km long. The time taken on the dirt road is 160 / (x - 30) hours.

According to the problem, the time taken on the return journey is 1 hour longer than the time taken on the outward journey. So we can set up the equation:

160 / (x - 30) = 210 / x + 1

To solve this equation, we can cross-multiply and simplify:

160x = 210(x - 30) + x(x - 30)

Simplifying further:

**160x = 210x