Question

Решите задачу с подробным объяснением пожалуйста. Теплоход за два дня прошёл 350 км. В первый день он был в пути 8 ч, а во второй- 6 ч. Какое расстояние он прошёл в каждый из дней, если он шёл с одинаковой скоростью?

Answer 1

8+6=14 часов был в пути теплоход
350:14=25 км\ч скорость теплохода
25*8=200 км прошел в первый день теплоход
25*6=150 км прошел во второй день теплоход.

Answer 2

Problem Analysis

We are given that a boat traveled a total distance of 350 km in two days. On the first day, it traveled for 8 hours, and on the second day, it traveled for 6 hours. We need to find the distance traveled on each day, assuming the boat traveled at a constant speed.

Solution

Let's assume the distance traveled on the first day is x km. Since the boat traveled for 8 hours on the first day, we can use the formula distance = speed × time to find the speed of the boat. Therefore, the speed of the boat is x/8 km/h.

Similarly, on the second day, the boat traveled for 6 hours. Let's assume the distance traveled on the second day is y km. Using the same formula, we can find the speed of the boat on the second day, which is y/6 km/h.

Since the boat traveled a total distance of 350 km, we can write the equation x + y = 350.

Now, we have two equations: 1. x/8 = y/6 (equating the speeds on both days) 2. x + y = 350 (total distance traveled)

We can solve these equations simultaneously to find the values of x and y.

Solving the Equations

To solve the equations, we can use the method of substitution. Rearranging the first equation, we get x = (8/6)y. Substituting this value of x into the second equation, we have (8/6)y + y = 350.

Simplifying the equation, we get (14/6)y = 350. Multiplying both sides by 6/14, we find y = (6/14) × 350.

Evaluating this expression, we find y = 150 km. Substituting this value of y back into the equation x = (8/6)y, we find x = (8/6) × 150.

Evaluating this expression, we find x = 200 km.

Answer

Therefore, the boat traveled 200 km on the first day and 150 km on the second day, assuming it traveled at a constant speed.

Verification

Let's verify our answer using the given information. The boat traveled for 8 hours on the first day at a speed of 200/8 = 25 km/h. Therefore, the distance traveled on the first day is 25 km/h × 8 h = 200 km.

Similarly, on the second day, the boat traveled for 6 hours at a speed of 150/6 = 25 km/h. Therefore, the distance traveled on the second day is 25 km/h × 6 h = 150 km.

Our answer is consistent with the given information, so we can conclude that the boat traveled 200 km on the first day and 150 km on the second day.

Conclusion

The boat traveled 200 km on the first day and 150 km on the second day, assuming it traveled at a constant speed.