Question

Автобус запізнювався на 15 хв. Щоби прибути до зупинки вчасно, він за 70 км до цієї станції збільшив свою швидкість на 14 км/год. Знайдіть початкову швидкість автобуса. У відповідь запишіть швидкість у км/год.

Answer 1

Пояснення:

15 хвилин=1/4 години.

Нехай початкова швидкість автобуса дорівнює х км/год >0.     ⇒

$\displaystyle \\\frac{70}{x} -\frac{70}{x+14} =\frac{1}{4} \\\\70*4*(x+14)-70*4*x=1*x*(x+14)\\\\280x+3920-280x=x^2+14x\\\\x^2+14x-3920=0\\\\x^2+70x-56x-3920=0\\\\x*(x+70)-56*(x+70)=0\\\\(x+70)*(x-56)=0\\\\x+70=0\\\\x_1=-70\notin\\\\x-56=0\\\\x_2=56.$

Відповідь: початкова швидкість автобуса дорівнює 56 км/год.

Answer 2

To find the initial speed of the bus, we can use the formula:

Initial Speed = Final Speed - Change in Speed

Given that the bus increased its speed by 14 km/h and traveled a distance of 70 km, we can substitute these values into the formula:

Initial Speed = Final Speed - Change in Speed Initial Speed = Final Speed - 14 km/h

Now, we need to find the final speed of the bus. We know that the bus was delayed by 15 minutes, which is equivalent to 0.25 hours. To calculate the final speed, we can use the formula:

Final Speed = Distance / Time

The distance traveled by the bus is 70 km, and the time taken is the original time plus the delay of 0.25 hours. Therefore:

Final Speed = 70 km / (Time + 0.25 hours)

Now, we can substitute the value of the final speed into the initial speed formula:

Initial Speed = (70 km / (Time + 0.25 hours)) - 14 km/h

To find the initial speed, we need to know the original time it took for the bus to travel the 70 km distance. Unfortunately, the original time is not provided in the question. Therefore, we cannot calculate the initial speed without this information.

If you have any additional information or if there is anything else I can help you with, please let me know!