A distance of 630 km, a car travels 2 hours faster than a motorcyclist. During the time it takes for the car to travel 45 km

| January 9, 2021 | education

A distance of 630 km, a car travels 2 hours faster than a motorcyclist. During the time it takes for the car to travel 45 km, the motorcycle will have time to cover 35 km. Find the speed of the motorcycle.

Suppose that the speed of the car is x km / h, so it will cover 630 km in 630 / x hours.
Let the motorcyclist’s speed be equal to y km / h, which means that he will travel 630 km in 630 / y hours.
By the condition of the problem, we can compose a system of two equations:
630 / y – 630 / x = 2,
45 / x = 35 / y.
From the second equation we get:
35 * x = 45 * y,
x = 45 * y / 35 = 9 * y / 7.
Substitute this x value in the first equation:
630 / y – 630: 9 * y / 7 = 2,
630 / y – 630 * 7/9 * y = 2,
630 / y – 490 / y = 2,
140 / y = 2,
y = 140/2,
y = 70 (km / h) – motorcycle speed.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.