Question

Nick's dad wanted to measure the length of his backyard and asked Nick to do this with his footsteps. Since it was winter, they were able to count their footprints in the snow starting from the end of the backyard moving in the same direction towards the front. In some places, Nick and his dad's footprints coincided. Eventually, they counted 67 footprints, including their first step. What is the length of the backyard in meters, if the Nick's footstep is 51 cm long and his dad's is 68 cm long?

Answer 1

2244 cm

Explanation:

The first first thing we must do is find the LCM of the following numbers

(51; 68) = 204.

This means that the first time they coincide is at 204.

Now, since his steps always coincide after 204

In Nick's case

Nick's 204 ÷ 51 = 4th step

and in the case of the father

204 ÷ 68 of his father = 3rd step.

Which means that in the 204 cm distance, there will be a total of 6 foot steps, except in the first 204 cm when your "initial" step is counted.

Replacing these values we have that the total distance will be:

67-1 (initial step) / (6 * 204) = 2244 cm