Question

В 8 часов утра из города A в город B вышел автобус со скоростью 56 км в час, а в 11часов дня из B в A вышел грузовик со скоростью 32 км в час. В какое время и на каком расстоянии от города A они встретились, если расстояние между городами 520 км?

Answer 1

11-8=3часа  автобус был в пути до того как из В выехал грузовик
56*3=168км проехал автобус за 3 часа
520-168=352км осталось проехать
56+32=88км/ч скорость сближения
352:88=3часа -время через которое грузовик встретил автобус
11+3=14часов дня произошла встреча
168+(56*3)=168+168=336км от города А автобус встретился с грузовиком

Answer 2

Problem Analysis

To solve this problem, we need to find the time and distance at which the bus and the truck meet. The bus travels from city A to city B at 56 km/h, and the truck travels from city B to city A at 32 km/h. The distance between the cities is 520 km.

Solution

Let's denote the time at which the bus and the truck meet as t hours after 8 am. We can use the formula: Distance = Speed × Time to calculate the distance traveled by each vehicle.

The distance traveled by the bus in t hours can be calculated as: Distance by bus = Speed of bus × t

The distance traveled by the truck in (t - 3) hours (as the truck starts at 11 am, 3 hours after the bus) can be calculated as: Distance by truck = Speed of truck × (t - 3)

Given that the sum of the distances traveled by the bus and the truck is equal to the total distance between the cities (520 km), we can form the equation: Distance by bus + Distance by truck = 520

Calculations

Let's substitute the given speeds and times into the equation and solve for t.

Distance by bus = 56t Distance by truck = 32(t - 3) 56t + 32(t - 3) = 520 56t + 32t - 96 = 520 88t - 96 = 520 88t = 616 t = 7

Answer

The bus and the truck will meet after 7 hours from 8 am, which is at 3 pm. To find the distance at which they meet, we can substitute t = 7 into the distance formula for the bus or the truck.

Distance = Speed × Time Distance = 56 × 7 Distance = 392 km

So, they will meet at 3 pm and the distance from city A at which they meet is 392 km.

I hope this helps! If you have further questions, feel free to ask.