Question

Теплоход за два дня прошёл 375 км. в первый день он был в пути 8 ч, а во второй 7 ч. Какое расстояние он прошёл в каждый из дней, если шёл с одинаковой средней скоростью?

Answer 1

8 + 7 = 15 - часов время в пути
375 : 15 = 25 км/час - скорость
25 х 8 = 200 км - первый день
25 х 7 = 175 км - второй день

Answer 2

375:(8+7)=25 км в час (скорость теплохода)
8*25=200 км (прошел в первый день)
7*25=175 км (прошел во второй день)

Answer 3

Problem Analysis

We are given that a boat traveled a total distance of 375 km in two days. On the first day, it was in motion for 8 hours, and on the second day, it was in motion for 7 hours. We need to determine the distance traveled each day, assuming the boat maintained a constant average speed.

Solution

To find the distance traveled each day, we can use the formula:

Distance = Speed × Time

Let's assume the boat traveled x km on the first day and y km on the second day. Since the boat traveled at the same average speed on both days, we can set up the following equations:

x = Speed × 8 (Equation 1)

y = Speed × 7 (Equation 2)

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

Solving the Equations

To solve the equations, we can divide Equation 1 by Equation 2:

(x / y) = (Speed × 8) / (Speed × 7)

Simplifying the equation:

(x / y) = 8 / 7

Cross-multiplying:

7x = 8y

Rearranging the equation:

x = (8y) / 7 (Equation 3)

Now, we can substitute Equation 3 into Equation 1:

(8y) / 7 = Speed × 8

Simplifying the equation:

y = (7 × Speed) / 8 (Equation 4)

Finding the Distance Traveled Each Day

We have two equations, Equation 3 and Equation 4, that relate the distances traveled each day to the average speed of the boat. We can use these equations to find the values of x and y.

Let's substitute Equation 4 into Equation 3:

x = (8 × [(7 × Speed) / 8]) / 7

Simplifying the equation:

x = Speed

Therefore, the distance traveled on the first day (x) is equal to the average speed of the boat.

Similarly, substituting Equation 4 into Equation 4:

y = (7 × Speed) / 8

Therefore, the distance traveled on the second day (y) is equal to (7/8) times the average speed of the boat.

Answer

Based on the given information, the boat traveled x km on the first day and y km on the second day, where:

x = Speed

y = (7/8) × Speed

Since the boat traveled a total distance of 375 km in two days, we can set up the following equation:

x + y = 375

Substituting the values of x and y:

Speed + (7/8) × Speed = 375

Combining like terms:

(15/8) × Speed = 375

Simplifying the equation:

Speed = (375 × 8) / 15

Calculating the value of Speed:

Speed = 200 km/h

Therefore, the boat traveled 200 km on the first day and (7/8) × 200 = 175 km on the second day.

Conclusion

The boat traveled 200 km on the first day and 175 km on the second day, assuming it maintained a constant average speed.

Please let me know if I can help you with anything else.