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?

Question

Mathematics

Scarlet

2 June, 23:02

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?

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Answers (1)

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Shania Holmes · Answer 1

22.44 meters

Step-by-step explanation:

Solution:

First find LCM (51,68) = 204.

So their footsteps coincide every time after Nick's 204:51 = 4th step and his dad's 204:68 = 3rd step.

So, in the distance of 204 cm, there will be total 6 footsteps, except in the first 204 cm when their "starting" step is counted.

The total distance will be 67 - 1 (starting step) / 6 · 204 = 2244 cm or 22.44m.