The radius of the front wheel of the carriage is 0.25 m, and the radius of the rear wheel is 0.6 m.

The radius of the front wheel of the carriage is 0.25 m, and the radius of the rear wheel is 0.6 m. What distance did the carriage travel if its rear wheel made 280 revolutions less than the front one?

Find the circumference of the front and rear wheels.

C = 2πR = 2 ∙ 3.14 ∙ 0.25 = 1.57 meters – front wheel.

C = 2πR = 2 ∙ 3.14 ∙ 0.6 = 3.768 meters – rear wheel.

Let’s denote the number of revolutions made by the rear wheel – x, then the front wheel made (x + 280) revolutions. The distance traveled by the front wheel is 1.57 (x + 280). And the distance traveled by the rear wheel is 3.768x. These distances are the same. Let’s find the number of revolutions using the equation.

1.57 (x + 280) = 3.768x;

1.57x + 439.6 = 3.768x;

3.768x – 1.57x = 439.6;

2.198x = 439.6.

x = 200 revolutions – done by the rear wheel.

Then the front wheel made x + 280 = 200 + 280 = 480 rpm.

Let’s find the distance that the carriage has traveled.

3.768x = 3.768 ∙ 200 = 753.6 meters.

Answer: the carriage traveled 753.6 meters.