Question

поезд прошёл расстояние между двумя городами за 8 часов.Половину пути поезд шёл со скоростью 40 км/ч, а другую половину - со скоростью 60км/ч.Сколько часов шёл поезд с каждой скоростью отдельно?

Answer 1

Со скоростью 40 он шел x часов и прошел 40x км.
Со скоростью 60 он шел y часов и прошел 60y км.
А всего за 8 часов.
x + y = 8
А путь одинаковый, это половина пути АВ
40x = 60y
y = 4x/6 = 2x/3
Подставляем
x + 2x/3 = 8
(3x + 2x)/3 = 5x/3 = 8
x = 3*8/5 = 24/5 = 4,8 часов шел поезд со скоростью 40
y = 2x/3 = 2*4,8/3 = 2*1,6 = 3,2 часов шел поезд со скоростью 60..

Answer 2

Calculating Train Speeds

To solve this problem, we can use the formula:

distance = speed × time

Let's denote the time the train traveled at 40 km/h as t1 and the time it traveled at 60 km/h as t2. We know that the total time taken is 8 hours, so we can express this as an equation:

t1 + t2 = 8

We also know that the distance traveled at both speeds is the same, so we can express this as another equation:

40t1 = 60t2

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

Solving for t1 and t2

Using the equation 40t1 = 60t2, we can express t1 in terms of t2:

t1 = (60/40)t2

Substituting this into the equation t1 + t2 = 8, we get:

(60/40)t2 + t2 = 8

Solving for t2: (3/2)t2 + t2 = 8 (5/2)t2 = 8 t2 = 8 * (2/5) t2 = 3.2 hours

Substituting t2 back into the equation t1 = (60/40)t2: t1 = (60/40) * 3.2 t1 = 4.8 hours

So, the train traveled at a speed of 40 km/h for 4.8 hours and at a speed of 60 km/h for 3.2 hours.

This calculation is based on the given information and the application of the formula for distance, speed, and time.