Question

Екі автомобиль бірдей жылдамдық пен қозғалды. Біріншісі 400 км, ал екіншісі 480 км жүріп өтті. Егер бірінші автомобиль екіншіге қарағанда 2 сағат кем жүрсе, әрқайсысы қанша уақыт жүрген?

Answer 1

1 екi сагат екiнщ I 2

Answer 2

Calculation of Time Traveled

To calculate the time traveled by the first car and the second car, we need to determine their respective speeds. We can do this by dividing the distance traveled by each car by the time it took to cover that distance.

Let's assume that the speed of the first car is x km/h and the speed of the second car is y km/h.

The first car traveled a distance of 400 km and the second car traveled a distance of 480 km. We also know that when the first car catches up to the second car, it takes 2 hours less time to cover the same distance.

Using the formula distance = speed × time, we can set up the following equations:

For the first car: 400 = x × t1 (Equation 1)

For the second car: 480 = y × t2 (Equation 2)

Where t1 is the time taken by the first car and t2 is the time taken by the second car.

We also know that when the first car catches up to the second car, it takes 2 hours less time to cover the same distance. Therefore, we can write:

t2 = t1 - 2 (Equation 3)

To solve this system of equations, we can substitute Equation 3 into Equation 2:

480 = y × (t1 - 2)

Simplifying this equation, we get:

480 = y × t1 - 2y

Now, let's solve this equation for y:

480 + 2y = y × t1

2y = y × t1 - 480

2y = y(t1 - 480)

y = (t1 - 480)/2 (Equation 4)

Now, let's substitute Equation 4 into Equation 1:

400 = x × t1

Simplifying this equation, we get:

x = 400/t1 (Equation 5)

Now, we have expressions for x and y in terms of t1. We can substitute these expressions into Equation 4 to solve for t1:

(t1 - 480)/2 = 400/t1

Cross-multiplying, we get:

t1^2 - 480t1 = 800

Rearranging the equation, we get:

t1^2 - 480t1 - 800 = 0

Now, we can solve this quadratic equation to find the value of t1.