Question

Велосипедист каждую минуту проезжает на 500 м меньше,чем мотоциклист,поэтому на путь в 120 км. он затрачивает времени на 2 часа больше,чем мотоциклист. Найдите скорость мотоцикла

Answer 1

500 м=0,5 км

60*0,5=30 км/ч

v-cкорость мотоциклиста

v-30 скорость велосипедиста

120/v+2=120/(v-30)

v=60

ответ скорость мотоцикла 60 км/ч

Answer 2

Calculating the Motorcycle's Speed

To find the speed of the motorcycle, we can use the following approach:

Let's assume the speed of the motorcyclist is x km/h and the speed of the cyclist is (x - 500) km/h.

Given that the distance is 120 km, the time taken by the motorcyclist is 120 / x hours, and the time taken by the cyclist is 120 / (x - 500) hours.

We also know that the cyclist takes 2 hours longer than the motorcyclist, so we can set up the equation:

120 / (x - 500) = 120 / x + 2

Solving this equation will give us the speed of the motorcycle.

Solving the Equation

Let's solve the equation step by step:

120 / (x - 500) = 120 / x + 2

First, let's find a common denominator:

120x = 120(x - 500) + 2x(x - 500)

Expanding and simplifying the equation:

120x = 120x - 60000 + 2x^2 - 1000x

Combining like terms:

0 = 2x^2 - 1000x - 60000

Now, we have a quadratic equation in the form ax^2 + bx + c = 0. We can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 2, b = -1000, and c = -60000.

Calculating the Speed

Using the quadratic formula, we can calculate the speed of the motorcycle.