Two jet planes simultaneously started traveling in opposite directions from the same airport. four hours later they were 3800 miles apart. find the rate of each plane, if one of them traveled 80 miles per hour faster than the other.

Rate of travelling of the 2 planes = 435 mph and 515 mph

Step-by-step explanation

d1 + d2 = 3800     (where d1 and d2 are the distances travelled by  each plane).

Let v1 = velocity of first plane so v1 + 80 will be velocity of the second)

They both travelled for 4 hours

Distance = time * speed.

So  d1 = 4v1  and  d2 = 4(v1 + 80)

Substituting for d1 and d2 in the first equation:-

4v1 + 4(v1 + 80) = 3800

8v1 + 320 = 3800

8v1 =  3480

v1 =  435 mph

and  v1 + 80 = 515 mph

∠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.