Question

Расстояние в 40 км такси преодолело на 10 мин быстрее чем автобус.какова скорость каждого, если скорость такси в 20км/ч больше скорости автобуса

Answer 1

Пусть x км/ч - скорость автобуса, тогда скорость такси: (x+20) км/ч
Время автобуса: $\dfrac{S}{v} = \dfrac{40}{x}$

Время такси $\dfrac{S}{v} = \dfrac{40}{x+20}$

Разница между ними состоит 10 минут, то есть, составим уравнение
$\dfrac{40}{x} -\dfrac{40}{x+20} = \dfrac{10}{60} \\ \\ \\ \dfrac{1}{x} - \dfrac{1}{x+20} =\dfrac{1}{240} \,\, \bigg|\cdot240x(x+20)\\ \\ \\ 240(x+20)-240x=x(x+20)\\ \\ 240x+240\cdot20-240x=x^2+20x\\ \\ x^2+20x-240\cdot20=0\\ \\ (x+10)^2-100-240\cdot20=0\\ \\ (x+10)^2=100\cdot(1+24\cdot 2)\\ \\ (x+10)^2=100\cdot49\\ \\ x+10=\pm10\cdot7$
Это уравнение будет удовлетворять условию, если
$x+10=10\cdot7\\ x=60$
Итак, 60 км/ч - скорость автобуса, тогда скорость такси будет $(60+20)=80$ км/ч

Answer 2

Calculating the Speed of Taxi and Bus

To calculate the speed of the taxi and the bus, we can use the following information:

- The distance traveled is 40 km. - The taxi took 10 minutes less than the bus to cover this distance. - The speed of the taxi is 20 km/h faster than the speed of the bus.

Let's denote the speed of the bus as x km/h and the speed of the taxi as (x + 20) km/h.

Calculating the Time Taken by Taxi and Bus

We know that time = distance / speed. Using this formula, we can calculate the time taken by the taxi and the bus to cover the 40 km distance.

The time taken by the taxi is: 40 / (x + 20) hours

The time taken by the bus is: 40 / x hours

Forming the Equation

Given that the taxi took 10 minutes (1/6 hours) less time than the bus, we can form the equation:

40 / (x + 20) = 40 / x - 1/6

Solving the Equation

We can solve this equation to find the value of x and then calculate the speed of the taxi.

I will now calculate the speed of the taxi and the bus using the provided information.