Question

Iз Киева до Днiпропетровська вирушив потяг iз швидкiстю 63 км.год,а через 3 години йому назустрiч iз Днiпропетровська вирушив експрес зi швидкiстю 109 км.год.Через який час пiсля того,як вирушив експрес потяги зустрiлися i на якiй вiдстанi вiд Киева вiдбулася ця зустрiч,якщо вiдстань мiж Киевом i Днiпропетровськом 533 км ?

Answer 1

1)63*3=189 км проїхав потяг із Київа до виходу потяга із Дніпра
2)533-189=344 км треба подолати потягам до зустрічи
3)63+109=172 км /год швидкість наближення
4)344:172=2 год -через цей час відбудеться зустріч
5)109*2=218 км подолає потяг із Дніпра за 2 год
6)533-218=315 км на цій відстані від Київа відбудеться зустріч
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Answer 2

Problem Analysis

We are given that a train departs from Kyiv to Dnipro at a speed of 63 km/h, and after 3 hours, an express train departs from Dnipro to Kyiv at a speed of 109 km/h. We need to determine the time it takes for the trains to meet and the distance from Kyiv where this meeting occurs. The distance between Kyiv and Dnipro is given as 533 km.

Solution

Let's denote the time it takes for the trains to meet as 't' hours. Since the first train has been traveling for 3 hours before the second train starts, the total time traveled by the first train is 't + 3' hours.

To find the distance traveled by each train, we can use the formula: distance = speed × time.

For the first train: distance1 = speed1 × time1 distance1 = 63 km/h × (t + 3) hours

For the second train: distance2 = speed2 × time2 distance2 = 109 km/h × t hours

Since the total distance traveled by both trains is equal to the distance between Kyiv and Dnipro (533 km), we can write the equation: distance1 + distance2 = 533 km

Substituting the values of distance1 and distance2, we get: 63 km/h × (t + 3) hours + 109 km/h × t hours = 533 km

Simplifying the equation: 63t + 189 + 109t = 533 172t = 533 - 189 172t = 344 t = 344 / 172 t = 2

Therefore, the trains will meet after 2 hours. To find the distance from Kyiv where this meeting occurs, we can substitute the value of 't' into the equation for distance1: distance1 = 63 km/h × (t + 3) hours distance1 = 63 km/h × (2 + 3) hours distance1 = 63 km/h × 5 hours distance1 = 315 km

So, the trains will meet 315 km from Kyiv.

Answer

The trains will meet after 2 hours and the meeting point is 315 km from Kyiv.

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