Question

моторная лодка на 21 км по течению реки и обратно затратила 2 часа 40 минут. в другой раз та же лодка прошла по течению реки 18 км и 14 против течения, затратив 2 часа. Какова собственная скорост лодки и скорость течения реки

Answer 1

2 часа 40 минут = 8/3 часа Пусть скорость лодки по течению х, а скорость против течения - у. Тогда для первого раза 21/х + 21/у = 8/3 а для второго раза 18/х + 14/у = 2 х и у положительные Умножим первое ур-е на 3ху, а второе на 4ху получим 63у + 63х = 8ху 72у + 56х = 8ху (отнимем от второго первое) 9у - 7х = 0 18/х + 14/у = 2 9у=7х 18/х + 14/у = 2 х=9у/7 18*7/9у + (14*9)9у= 2 х=9у/7 (126 +126)/9у=2 (умножим на 9у) 18у=252 х=9у/7 у=14 х=18 18 -14 =4 (км/ч) удвоенная скорость течения 4 :2=2 (км/ч) скорость течения 14 +2 =16 (км/ч) скорость лодки

Answer 2

Calculating Boat's Speed and River's Current

To calculate the boat's speed and the river's current, we can use the given information about the distances traveled and the time taken in both scenarios.

Let's denote the boat's speed as b and the river's current speed as c.

1. Upstream and Downstream Travel: - The boat's speed relative to the water when traveling downstream is b + c. - The boat's speed relative to the water when traveling upstream is b - c.

2. Given Information: - When the boat traveled 21 km downstream and back, it took 2 hours and 40 minutes. - When the boat traveled 18 km downstream and 14 km upstream, it took 2 hours.

Calculating Boat's Speed

Using the given information, we can set up the following system of equations to solve for the boat's speed:

1. Downstream and Upstream Travel Time Equations: - For the 21 km downstream and back trip: - \( \frac{21}{b+c} + \frac{21}{b-c} = 2.67 \) hours (2 hours and 40 minutes) - For the 18 km downstream and 14 km upstream trip: - \( \frac{18}{b+c} + \frac{14}{b-c} = 2 \) hours

Solving these equations will give us the boat's speed relative to the water.

Let's proceed with solving these equations to find the boat's speed and the river's current speed.