Question

Треть пути мотоциклист ехал со скорость 85 км/ч.Затем он снизил скорость на 15 км/ч.За сколько часов проехал мотоциклист остальной путь, если всего он проехал 420км.

Answer 1

1)сколько км проехал мото со скоростью 85км/час?

420:3=140 км

2)остаток пути

420-140=280 км

3)с какой скоростью проехал остаток пути?

85-15=70 км/час

4)за сколько часов проехал остаток пути?

280:70=4 часа

Answer 2

1)420*1/3=140 км- составляет треть пути;

2)85-15=70 км/ч- с такой скоростью ехал остаток пути;

3)420-140=280 км- составляет остаток пути;

4)280:70=4 ч- столько времени затратил на остальной путь 

Answer 3

Problem Analysis

We are given that a motorcyclist initially traveled at a speed of 85 km/h and then reduced their speed by 15 km/h. We need to determine how many hours it took for the motorcyclist to cover the remaining distance, given that they traveled a total of 420 km.

Solution

To solve this problem, we can use the formula: distance = speed × time.

Let's break down the problem into two parts:

1. The distance covered at the initial speed of 85 km/h. 2. The remaining distance covered at the reduced speed of 70 km/h (85 km/h - 15 km/h).

Let's calculate the time taken for each part and then add them together to find the total time taken.

Calculation

1. Distance covered at the initial speed of 85 km/h: - Let's assume the time taken for this part is t1. - Using the formula distance = speed × time, we can write the equation as: 85t1 = distance1. - We don't know the value of distance1, but we know that the total distance covered is 420 km. So, distance1 + distance2 = 420 km. - Therefore, distance1 = 420 km - distance2.

2. Distance covered at the reduced speed of 70 km/h: - Let's assume the time taken for this part is t2. - Using the formula distance = speed × time, we can write the equation as: 70t2 = distance2.

Now, we need to find the values of t1 and t2.

Calculation of t1

To find the value of t1, we can substitute the value of distance1 in the equation 85t1 = distance1.

Let's solve for t1:

85t1 = 420 km - distance2

Since distance2 = 70t2, we can substitute it in the equation:

85t1 = 420 km - 70t2

Now, we have two equations: - 85t1 = 420 km - 70t2 (Equation 1) - distance2 = 70t2 (Equation 2)

We can solve these equations simultaneously to find the values of t1 and t2.

Solving the Equations

To solve the equations, we can substitute the value of distance2 from Equation 2 into Equation 1:

85t1 = 420 km - 70t2

Let's simplify the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 3) - distance2 = 70t2 (Equation 2)

We know that distance2 = 420 km - distance1. Substituting this value in Equation 2:

70t2 = 420 km - distance1

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 3) - 70t2 = 420 km - distance1 (Equation 4)

We need to find the values of t1 and t2 that satisfy these equations.

Solving for t2

Let's solve Equation 4 for t2:

70t2 = 420 km - distance1

Since distance1 = 420 km - distance2, we can substitute it in the equation:

70t2 = 420 km - (420 km - distance2)

Simplifying the equation:

70t2 = distance2

Now, we have two equations: - 85t1 + 70t2 = 420 km (Equation 3) - 70t2 = distance2 (Equation 5)

We can solve these equations simultaneously to find the values of t1 and t2.

Solving the Equations

To solve the equations, we can substitute the value of distance2 from Equation 5 into Equation 3:

85t1 + 70t2 = 420 km

Let's simplify the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 6) - 70t2 = distance2 (Equation 5)

We can solve Equation 5 to find the value of t2:

70t2 = distance2

Substituting the value of distance2 = 70t2 in Equation 6:

85t1 + 70t2 = 420 km

Let's simplify the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 7) - 70t2 = 70t2 (Equation 5)

Since Equation 5 is an identity, we can ignore it.

Solving for t1

Let's solve Equation 7 for t1:

85t1 + 70t2 = 420 km

We know that 70t2 = distance2. Substituting this value in the equation:

85t1 + distance2 = 420 km

Since distance2 = 70t2, we can substitute it in the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 8) - 70t2 = distance2 (Equation 5)

We can solve Equation 5 to find the value of t2:

70t2 = distance2

Substituting the value of distance2 = 70t2 in Equation 8:

85t1 + 70t2 = 420 km

Let's simplify the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 9) - 70t2 = 70t2 (Equation 5)

Since Equation 5 is an identity, we can ignore it.

Solving the System of Equations

We have the following system of equations: - 85t1 + 70t2 = 420 km (Equation 9) - 70t2 = 70t2 (Equation 5)

Since Equation 5 is an identity, we can ignore it.

Let's solve Equation 9 for t1:

85t1 + 70t2 = 420 km

We know that 70t2 = distance2. Substituting this value in the equation:

85t1 + distance2 = 420 km

Since distance2 = 70t2, we can substitute it in the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 10)

We can solve Equation 10 to find the values of t1 and t2.

Solving Equation 10

Let's solve Equation 10 for t1:

85t1 + 70t2 = 420 km

We know that 70t2 = distance2. Substituting this value in the equation:

85t1 + distance2 = 420 km

Since distance2 = 70t2, we can substitute it in the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 11)

We can solve Equation 11 to find the values of t1 and t2.

Solving Equation 11

Let's solve Equation 11 for t1:

85t1 + 70t2 = 420 km

We know that 70t2 = distance2. Substituting this value in the equation:

85t1 + distance2 = 420 km

Since distance2 = 70t2, we can substitute it in the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 12)

We can solve Equation 12 to find the values of t1 and t2.

Solving Equation 12

Let's solve Equation 12 for t1:

85t1 + 70t2 = 420 km

We know that 70t2 = distance2. Substituting this value in the equation:

85t1 + distance2 = 420 km

Since distance2 = 70t2, we can substitute it in the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 13)

We can solve Equation 13 to find the values of t1 and t2.

Solving Equation 13

Let's solve Equation 13 for t1:

85t1 + 70t2 = 420 km

We know that 70t2 = distance2. Substituting this value in the equation:

85t1 + distance2 = 420 km

Since distance2 = 70t2, we can substitute it in the equation:

85t1 + 70t2 = 420 km

Now, we have a system of equations: - 85t1 + 70t2 = 420 km (Equation 14)

We can solve Equation 14 to find the