Working alone, it takes Scott 16 minutes to inflate twenty balloons, Ashley can inflate the same twenty balloons in 15 minutes. Find how long it would take them if they worked together.

7.74 minutes

Step-by-step explanation:

Scott's rate = 20 /16 = 1.25

Ashley's rate = 20 / 15 = 1.333

Combined rate = (1.25 + 1.3333) = 2.583333

Hence, time it will take to inflate 20 balloons :

Rate = number of balloons / time taken

2.583333 = 20 / time taken

Time taken = 20 / 2.583333

Time taken = 7.7419

It will take them approximately 7.7 minutes to inflate 20 balloons

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.