Afather and his two sons wanted to measure the distance between the two tallest trees in the city garden by their footsteps. it was winter, and there was fresh snow in the garden, so they decided to start measuring from the same tree by walking one after another straight to the other tree. the father's footstep is 32 inches long, while the same for his sons is 28 inches and 24 inches. in what distance, in feet, the three steps would overlap the first time?

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The exercise is basically asking you to find the least common multiple of 32, 28 and 24.

In fact, by definition, that would be the first number that you will meet counting by 32s, 28s and 24s.

To start, we have to find the prime factorization of all the numbers:

Now, we have to consider all primes appearing, i.e. 2, 3 and 7. If a prime appears in more than one number, we'll have to consider the highest exponent. So, the highest exponent of 2 is 5, while 3 and 7 only appear at the first power.

So, the least common multiple is

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)