Question

пассажирский поезд проходит растояние равное 480 км на 4 часа быстрее чем товарный. Найти скорость каждого поезда,если скорость товарного на 20 км/час меньше скорости пассажирского

Answer 1

Х скорость товарного 
х+20 скорость пассажирского  
480/х-480/(х+20)=4  
480х+9600-480х=4х²+80х  
4х²+80х-9600=0     х²+20х-2400=0     D=400+9600=100²  
х=(-20+100)/2=40км/час скорость товарного; второй корень уравнения <0, не подходит 

40+20=60км/час скорость пассажирского

Answer 2

Пускай скорость пассажирского поезда будет х км/ч. Тогда скорость товарного поезда будет х-20 км/ч. Время, за которое пассажирский поезд пройдёт 480 км, пусть будет у ч, тогда время товарного поезда будет у+4 ч. Имеем систему уравнений: х×у=480, (х-20)×(у+4)=480. х=480/у, ((480/у)-20)×(у+4)=480, ((480-20у)/у)×(у+4)=480, (480-20у)×(у+4)=480у, 480у+1920-20у^2-80у=480у, -20у^2-80у+1920=0, -у^2-4у+96=0, D=(-4)^2-4×(-1)×96=16+384=400, у1=(4-корень с 400)/(2×(-1))=(4-20)/(-2)=(-16)/(-2)=8, у2=(4+корень с 400)/(2×(-1))=(4+20)/(-2)=24/(-2)=-12. у2=-12 - не может быть ответом задачи, так как время не может быть отрицательным. Значит у=8, х=480/8=60. Имеем: скорость пассажирского поезда равна 60 км/ч, скорость товарно поезда равна 60-20=40 км/ч.

Answer 3

To solve this problem, let's denote the speed of the passenger train as "V" km/h and the speed of the freight (or goods) train as "V - 20" km/h (since the speed of the freight train is 20 km/h less than the passenger train).

We know that the distance traveled by both trains is the same, which is 480 km. We also know that the passenger train takes 4 hours less than the freight train to cover this distance.

Let's set up equations based on the information given:

1. Distance = Speed × Time

For the passenger train: Distance = 480 km Speed = V km/h Time = Time taken by the passenger train (in hours)

For the freight train: Distance = 480 km Speed = (V - 20) km/h Time = Time taken by the freight train (in hours)

2. Time difference between the two trains: Time taken by the passenger train = Time taken by the freight train - 4 hours

Now, we can set up the equations:

1. Passenger train: 480 km = V km/h × Time taken by the passenger train

2. Freight train: 480 km = (V - 20) km/h × Time taken by the freight train

3. Time difference: Time taken by the passenger train = Time taken by the freight train - 4 hours

Now, we need to solve these equations to find the values of V (speed of the passenger train) and V - 20 (speed of the freight train).

Let's start by solving the third equation for Time taken by the passenger train: Time taken by the passenger train = Time taken by the freight train - 4 hours

Now, substitute this expression for Time taken by the passenger train in the first equation:

480 km = V km/h × (Time taken by the freight train - 4 hours)

Next, we can rewrite the equation for the freight train's time in terms of V: Time taken by the freight train = 480 km / (V - 20) km/h

Now, substitute this expression for Time taken by the freight train in the previous equation:

480 km = V km/h × [480 km / (V - 20) km/h - 4 hours]

Now, we can solve this equation to find the value of V, which will give us the speed of the passenger train. Once we have V, we can find the speed of the freight train by subtracting 20 km/h from V.

Let's go ahead and solve this equation:

480 km = V × [480 km / (V - 20) - 4]

To simplify further, let's clear the fractions by multiplying everything by (V - 20):

480 km × (V - 20) = V × [480 km - 4(V - 20)]

Now, distribute on the right side:

480V - 9600 = 480V - 4V^2 + 80V

Combine like terms:

4V^2 - 560V + 9600 = 0

Now, this is a quadratic equation. We can solve for V using the quadratic formula:

V = [ -b ± sqrt(b^2 - 4ac) ] / 2a

where a = 4, b = -560, and c = 9600.

Let's calculate:

V = [ -(-560) ± sqrt((-560)^2 - 4 × 4 × 9600) ] / 2 × 4 V = [ 560 ± sqrt(313600 - 153600) ] / 8 V = [ 560 ± sqrt(160000) ] / 8 V = [ 560 ± 400 ] / 8

Now, we have two possible solutions for V:

1. V = (560 + 400) / 8 = 960 / 8 = 120 km/h
2. V = (560 - 400) / 8 = 160 / 8 = 20 km/h

However, the second solution V = 20 km/h doesn't make sense in this context because the problem states that the freight train's speed is 20 km/h less than the passenger train's speed. Therefore, the second solution is not valid.

So, the speed of the passenger train (V) is 120 km/h, and the speed of the freight train (V - 20) is 120 km/h - 20 km/h = 100 km/h.