Question

The durations in seconds of their first three flights can be represented by consecutive odd integers, such that the product of the first and third was equal to 4 led than five times the second. Find the durations of their first three flights.

Answer 1

Answer:

3 sec, 5 sec and 7 sec.

Step-by-step explanation:

The first important detail is ''consecutive odd integers'', which can be express as: $x; (x+2); (x+4)$

Then, we apply this definitions to the conventional language to convert it to math language:

The product of the first and third: $x(x+4)$

4 less than five times the second: $5(x+2) - 4$

So, the expression would be $x(x+4) = 5(x+2) -4$

If we solve this equation, will result: $x^{2}-x-6=0$; which is an second grade equation.

To solve it, we need to find two number that their multiplication results in 6, but their subtract results in 1. Being those numbers, 3 and 2.

$(x-3)(x+2)=0$

So, results are $x=3; x=-2$

But, time cannot be negative, so, we only take the first value.

If we substituted in the initial expression of the odd integers, we will have:

$3; (3+2); (3+4)$

Hence, the numbers are 3, 5 and 7.