Question

Из пункта А выехал всадник со скоростью 12 км/ч. Одновременно с ним из пункта В, находящегося на расстоянии 24 км от пункта А, вышел пешеход со скоростью 4 км/час .Пешеход и всадник движутся в одном направлении. На каком расстоянии от пункта В всадник догонит пешехода?

Answer 1

6 км. Находим общую скорость - 12+4=16 км/ч. 24 км они преодолеют за 24/16=1,5 ч. Т.е. встретятся через полтора часа (всадник догонит пешехода). Так как они будут на одном расстоянии от пункта В, то достаточно найти, сколько преодолел пешеход. 4*1,5=6 км.

Answer 2

Problem Analysis

We are given that a rider leaves point A with a speed of 12 km/h, while simultaneously a pedestrian leaves point B, which is 24 km away from point A, with a speed of 4 km/h. Both the rider and the pedestrian are moving in the same direction. We need to determine at what distance from point B the rider will catch up to the pedestrian.

Solution

To find the distance at which the rider catches up to the pedestrian, we need to calculate the time it takes for the rider to cover the distance between the two points.

Let's denote: - Distance between point A and point B as d_AB (which is 24 km) - Speed of the rider as v_rider (which is 12 km/h) - Speed of the pedestrian as v_pedestrian (which is 4 km/h) - Time taken by the rider to catch up to the pedestrian as t_catch_up - Distance at which the rider catches up to the pedestrian as d_catch_up

We can use the formula: distance = speed × time to calculate the time taken by the rider to catch up to the pedestrian.

The time taken by the rider to cover the distance between point A and point B is the same as the time taken by the pedestrian to cover the distance between point B and the point where they are caught up by the rider.

Therefore, we can set up the equation: d_AB = v_pedestrian × t_catch_up.

Solving this equation for t_catch_up, we get: t_catch_up = d_AB / v_pedestrian.

Now, we can substitute the values of d_AB and v_pedestrian into the equation to find t_catch_up.

Once we have the value of t_catch_up, we can calculate the distance at which the rider catches up to the pedestrian using the formula: d_catch_up = v_rider × t_catch_up.

Let's calculate the values.

Calculation

Given: - Distance between point A and point B, d_AB = 24 km - Speed of the rider, v_rider = 12 km/h - Speed of the pedestrian, v_pedestrian = 4 km/h

Using the formula t_catch_up = d_AB / v_pedestrian, we can calculate the time taken by the rider to catch up to the pedestrian.

Substituting the values, we get: t_catch_up = 24 km / 4 km/h = 6 hours.

Now, using the formula d_catch_up = v_rider × t_catch_up, we can calculate the distance at which the rider catches up to the pedestrian.

Substituting the values, we get: d_catch_up = 12 km/h × 6 hours = 72 km.

Answer

The rider will catch up to the pedestrian at a distance of 72 km from point B.

Conclusion

The rider will catch up to the pedestrian at a distance of 72 km from point B.