Question

Два мотоциклиста выезжают одновременно навстречу друг другу из пунктов М и Н расстояние между которыми 96 км и встречаются через час.С какой скоростью ехал каждый мотоциклист если через 20 мин после встречи первому оставался путь до Н втрое меньший чем второму до М?

Answer 1

1)96:2=48(км)-половина расстояния.
2)48:3=16(км/ч)-скорость второго мотоциклиста.
3)48-16=32(км/ч)-скорость первого мотоциклиста.
Ответ:16, 32 км/ч 

Answer 2

Problem Analysis

We have two motorcyclists traveling towards each other from points M and N, which are 96 km apart. They meet after one hour. After 20 minutes from the meeting, the first motorcyclist has a remaining distance to N that is three times smaller than the remaining distance of the second motorcyclist to M. We need to find the speeds at which each motorcyclist was traveling.

Solution

Let's assume that the speed of the first motorcyclist is x km/h and the speed of the second motorcyclist is y km/h.

To find the speeds, we can use the formula: speed = distance / time.

We know that the distance between M and N is 96 km and the time taken to meet is 1 hour. Therefore, the relative speed of the two motorcyclists is the sum of their speeds, which is equal to the distance divided by the time:

x + y = 96 / 1 = 96 km/h. After 20 minutes (1/3 of an hour) from the meeting, the first motorcyclist has a remaining distance to N that is three times smaller than the remaining distance of the second motorcyclist to M. Let's calculate the remaining distances:

The remaining distance for the first motorcyclist is 96 - x * (1/3) km.

The remaining distance for the second motorcyclist is 96 - y * (1/3) km.

According to the problem, the remaining distance for the first motorcyclist is three times smaller than the remaining distance for the second motorcyclist:

96 - x * (1/3) = 3 * (96 - y * (1/3)).

Simplifying the equation:

96 - x/3 = 288 - y/3.

Rearranging the equation:

x/3 - y/3 = 288 - 96.

x/3 - y/3 = 192.

Multiplying both sides of the equation by 3:

x - y = 576. Now we have a system of two equations with two variables:

x + y = 96 (Equation 1)

x - y = 576 (Equation 2)

We can solve this system of equations to find the values of x and y.

Adding Equation 1 and Equation 2:

(x + y) + (x - y) = 96 + 576.

Simplifying the equation:

2x = 672.

Dividing both sides of the equation by 2:

x = 336.

Substituting the value of x into Equation 1:

336 + y = 96.

Simplifying the equation:

y = 96 - 336.

y = -240.

Since speed cannot be negative, we discard the negative value of y.

Therefore, the speed of the first motorcyclist is 336 km/h and the speed of the second motorcyclist is 240 km/h.

Answer

The first motorcyclist was traveling at a speed of 336 km/h and the second motorcyclist was traveling at a speed of 240 km/h.