Question

Помогите задачу решить) теплоход затратил 5 часов вниз по течению реки от пункта А до пункта B. на обратный путь против течения он затратил 8 часов 20 минут. найдите собственную скорость теалохода, если путь от А до В 100 км.

Answer 1

1) 8 часов 20 мин-5 часов=3 ч 20 мин
2)100:3,20=31,25км:ч

Answer 2

Problem Analysis

We are given that a boat spent 5 hours traveling downstream from point A to point B, and 8 hours and 20 minutes traveling upstream from point B to point A against the current. The distance between points A and B is 100 km. We need to find the boat's speed.

Solution

Let's assume the boat's speed in still water is V km/h, and the speed of the current is Vc km/h.

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the boat's effective speed downstream is V + Vc km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the boat's effective speed upstream is V - Vc km/h.

We can use the formula distance = speed × time to calculate the distances traveled downstream and upstream.

From the given information, we have the following equations:

Downstream: (V + Vc) × 5 = 100 km Upstream: (V - Vc) × (8 + 20/60) = 100 km

Let's solve these equations to find the values of V and Vc.

Calculation

From the downstream equation, we can solve for V + Vc: (V + Vc) × 5 = 100 V + Vc = 100/5 V + Vc = 20 (Equation 1)

From the upstream equation, we can solve for V - Vc: (V - Vc) × (8 + 20/60) = 100 V - Vc = 100/(8 + 20/60) V - Vc = 100/(8 + 1/3) V - Vc = 100/(25/3) V - Vc = 100 × 3/25 V - Vc = 12 (Equation 2)

Now, we have a system of equations with two variables (V and Vc). We can solve this system of equations to find the values of V and Vc.

Adding Equation 1 and Equation 2, we get: (V + Vc) + (V - Vc) = 20 + 12 2V = 32 V = 32/2 V = 16 km/h

Substituting the value of V into Equation 1, we can solve for Vc: 16 + Vc = 20 Vc = 20 - 16 Vc = 4 km/h

Answer

Therefore, the boat's speed in still water is 16 km/h, and the speed of the current is 4 km/h.

Note: The solution assumes that the boat's speed remains constant throughout the journey and that the current's speed remains constant as well.