Question

Самолет вылетел с аэродрома со скоростью 500 км/ч . Через 2 часа с этого же аэродрома в том же направлении вылетел другой самолет со скоростью 700 км/ч. Через сколько часов после вылета второй самолет догонит первый?

Answer 1

1000+500t=700t

1000=700t-500t

1000=200t

t=1000:200

t=5ч

Answer 2

Problem Analysis

We are given two airplanes that take off from the same airport in the same direction. The first airplane has a speed of 500 km/h, and the second airplane has a speed of 700 km/h. We need to determine how many hours it will take for the second airplane to catch up to the first airplane.

Solution

To solve this problem, we can set up an equation based on the relative speeds of the two airplanes. Let's assume that it takes "t" hours for the second airplane to catch up to the first airplane.

The distance traveled by the first airplane in "t" hours is given by: Distance1 = Speed1 * t

The distance traveled by the second airplane in "t" hours is given by: Distance2 = Speed2 * t

Since the second airplane catches up to the first airplane, the distances traveled by both airplanes must be equal. Therefore, we can set up the following equation: Distance1 = Distance2

Substituting the expressions for Distance1 and Distance2, we get: Speed1 * t = Speed2 * t

Simplifying the equation, we find: Speed1 * t - Speed2 * t = 0

Factoring out "t" from both terms, we have: t * (Speed1 - Speed2) = 0

Since we are interested in the time it takes for the second airplane to catch up to the first airplane, we can ignore the case where "t" is equal to zero. Therefore, we can divide both sides of the equation by (Speed1 - Speed2) to solve for "t": t = 0 / (Speed1 - Speed2) = 0

This means that the second airplane will catch up to the first airplane instantaneously, or in other words, they will meet at the same point in space at the same time.

Answer

Based on the given information, the second airplane will catch up to the first airplane instantaneously, or in other words, they will meet at the same point in space at the same time. Therefore, the answer is 0 hours.

Please let me know if you need any further clarification.