Question

Грузовой автомобиль задержался на 12 мин на заправочной станции, а затем на расстоянии 60 км наверстал потерянное время, увеличив скорость на 15 км/ч. Найдите первоначальную скорость автомобиля.

Answer 1

Пусть начальная скорость автомобиля v км/ч, тогда его увеличенная скорость будет (v+15) км/ч
время, с которым он проехал на обычной скорости 60 км - t
тогда время с задержкой будет t-1/5

получаем систему:

$\left \{ {{60=vt} \atop {60=(v+15)(t- \frac{1}{5})}} \right. \\ \\ vt=(v+15)(t- \frac{1}{5})=60 \\ \\ vt=vt- \frac{v}{5} +15t-3 \\ \\ 15t- \frac{v}{5} -3=0 \\ 75t-v-15=0 \\ v=75t-15 \\ \\ 60=(75t-15)t \\ 75t^2-15t-60=0 \\ 5t^2-t-4=0 \\ D=1+80=81=9^2 \\ t= \frac{1\pm9}{10} = \left \{ {{t_1=1} \atop {t_2= -\frac{8}{10} }} \right. \\ \\ 60= v$

Ответ: 60 км/ч

Answer 2

Calculation of the Initial Speed of the Truck

To find the initial speed of the truck, we can use the information provided.

Given: - The truck was delayed for 12 minutes at the gas station. - The truck made up for the lost time by increasing its speed by 15 km/h over a distance of 60 km.

To calculate the initial speed of the truck, we can use the formula:

Initial Speed = Distance / Time

Let's calculate the initial speed of the truck step by step:

1. Convert the delay time from minutes to hours: - 12 minutes = 12/60 = 0.2 hours

2. Calculate the time taken to cover the distance of 60 km at the increased speed: - Time = Distance / Speed - Time = 60 km / (Increased Speed + Initial Speed)

3. Calculate the time taken to cover the distance of 60 km at the initial speed: - Time = Distance / Speed - Time = 60 km / Initial Speed

Since the time taken to cover the distance of 60 km at the increased speed is the same as the time taken to cover the distance of 60 km at the initial speed, we can equate the two equations:

60 km / (Increased Speed + Initial Speed) = 60 km / Initial Speed

Now, let's solve the equation to find the initial speed of the truck.

Note: The search results provided by You.com do not contain the necessary information to directly answer this question. Therefore, we will proceed with the calculation based on the given information.

Let's calculate the initial speed of the truck.