Question

Два мотоциклиста Вадим и Виталий договорились встретиться через 3 часа и отправились одновременно навстречу друг другу, причём Вадим ехал со скоростью на 19 км/ч больше скорости, с которой ехал Виталий. Найдите, с какими скоростями ехали Вадим и Виталий, если исходное расстояние между ними составляет 267 км.

Answer 1

$v_1 = v_2 + 19$

$S = 267$

$t = 3$

$v = v_1 + v_2 = v_1 + v_1 - 19 = 2v_1 - 19$

$v = \frac{S}{t} = \frac{267}{3} = 89$

$2v_1 - 19 = 89$

$v_1 = 54$

$v_2 = 54 - 19 = 35$

Answer 2

Problem Analysis

Two motorcyclists, Vadim and Vitaliy, agreed to meet in 3 hours and started traveling towards each other simultaneously. Vadim was traveling at a speed 19 km/h faster than Vitaliy. The initial distance between them is 267 km. We need to find the speeds at which Vadim and Vitaliy were traveling.

Solution

Let's assume the speed at which Vitaliy was traveling as x km/h. Since Vadim was traveling 19 km/h faster, his speed can be represented as x + 19 km/h.

We can use the formula distance = speed × time to calculate the distances traveled by Vadim and Vitaliy in 3 hours.

The distance traveled by Vadim can be calculated as (x + 19) × 3 km.

The distance traveled by Vitaliy can be calculated as x × 3 km.

According to the problem, the sum of the distances traveled by Vadim and Vitaliy should be equal to the initial distance between them, which is 267 km.

So, we can set up the following equation:

(x + 19) × 3 + x × 3 = 267

Now, let's solve this equation to find the values of x and x + 19.

Calculation

(x + 19) × 3 + x × 3 = 267

Simplifying the equation:

3x + 57 + 3x = 267

Combining like terms:

6x + 57 = 267

Subtracting 57 from both sides:

6x = 210

Dividing both sides by 6:

x = 35

So, Vitaliy was traveling at a speed of 35 km/h, and Vadim was traveling at a speed of 35 + 19 = 54 km/h.

Answer

Vitaliy was traveling at a speed of 35 km/h, and Vadim was traveling at a speed of 54 km/h.