Question

Из двух городов,расстояние между которыми 840км,вышли одновременно навстречу друг другу два поезда.Скорость первого поезда 100км\ч,второго на 10км\ч больше.Через сколько часов поезда встретятся ?

Answer 1

Problem Analysis

We have two trains traveling towards each other from two different cities. The distance between the cities is 840 km. The first train is traveling at a speed of 100 km/h, while the second train is traveling at a speed 10 km/h faster than the first train. We need to determine how many hours it will take for the trains to meet.

Solution

To solve this problem, we can use the formula: time = distance / speed.

Let's calculate the time it will take for the first train to meet the second train.

The distance the first train travels is the sum of the distances covered by both trains before they meet. Let's call this distance d.

The distance covered by the first train is d, and the distance covered by the second train is 840 - d.

The speed of the first train is 100 km/h, and the speed of the second train is 10 km/h faster, which is 110 km/h.

Using the formula time = distance / speed, we can calculate the time it will take for the first train to meet the second train:

time = d / 100

Similarly, the time it will take for the second train to meet the first train is:

time = (840 - d) / 110

Since both trains are traveling for the same amount of time, we can set these two equations equal to each other and solve for d:

d / 100 = (840 - d) / 110

Let's solve this equation to find the value of d.

Calculation

To solve the equation d / 100 = (840 - d) / 110, we can cross-multiply:

110d = 100(840 - d)

Simplifying the equation:

110d = 84000 - 100d

Adding 100d to both sides:

210d = 84000

Dividing both sides by 210:

d = 400

Answer

The trains will meet after traveling a distance of 400 km. To find the time it will take for the trains to meet, we can substitute this value of d into either of the two equations we derived earlier:

time = d / 100

Substituting d = 400:

time = 400 / 100 = 4 hours

Therefore, the trains will meet after 4 hours.

Conclusion

The two trains will meet after traveling for 4 hours.