Question

Трактор выехал от станции к деревне на 30мин раньше грузовика. Когда грузовик, обогнав трактор, прибыл в деревню, трактору оставалось еще 3 км. Найти скорость трактора, если ск-ть грузовика на 20км/ч больше, а расстояние 12 км.

Answer 1

Problem Analysis

We are given that a tractor left a station for a village 30 minutes before a truck. When the truck overtook the tractor and arrived at the village, the tractor still had 3 km left to travel. We need to find the speed of the tractor given that the speed of the truck is 20 km/h faster and the total distance is 12 km.

Solution

Let's assume the speed of the tractor is x km/h. Since the speed of the truck is 20 km/h faster, the speed of the truck is x + 20 km/h.

We can use the formula distance = speed × time to solve this problem.

The time taken by the tractor to reach the village is the same as the time taken by the truck to overtake the tractor and reach the village. Let's denote this time as t hours.

The distance covered by the tractor is (x × t) km, and the distance covered by the truck is ((x + 20) × t) km.

According to the given information, the distance covered by the tractor is 3 km less than the total distance of 12 km. So we have the equation:

(x × t) = 12 - 3

Simplifying this equation, we get:

xt = 9

We also know that the truck took 30 minutes (0.5 hours) less time than the tractor to reach the village. So we have the equation:

t - 0.5 = t

Simplifying this equation, we get:

0.5 = t

Now we have two equations:

1. xt = 9 2. 0.5 = t

We can solve these equations simultaneously to find the value of x and t.

Solution Steps

1. Substitute the value of t from equation 2 into equation 1. 2. Solve the resulting equation for x. 3. Calculate the speed of the tractor by substituting the value of x into the equation x + 20.

Let's solve the equations to find the speed of the tractor.

Solution

Substituting the value of t from equation 2 into equation 1:

x(0.5) = 9

Simplifying:

0.5x = 9

Dividing both sides by 0.5:

x = 9 / 0.5

Simplifying:

x = 18

The speed of the tractor is 18 km/h.

Now, substituting the value of x into the equation x + 20:

18 + 20 = 38

The speed of the tractor is 18 km/h, and the speed of the truck is 38 km/h.

Answer

The speed of the tractor is 18 km/h. The speed of the truck is 38 km/h.