Two trains leave the station at the same time, one heading east and the other west. the eastbound train travels at 80 miles per hour. the westbound train travels at 70 miles per hour. how long will it take for the two trains to be 420 miles apart? do not do any rounding.

Question: How long will it take for the two trains to be 420 miles apart if two trains leave at the same time one going east and the other going west, with speed 80 miles per hour and 70 miles respectively. The number of hours to take them to have a distance of 420 can be computed as follows:

Let x= the number of hours

80x+70x=420

150x=420

x=420/150

x=2.8 hours

∠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.

a - base

b - exponent

so,