Two kids at a summer camp, Tina and Winston, are competing in a potato sack race. Tina is younger, so she is given a head start of 33 meters. When the race starts, Tina hops at a rate of 1 meter per second, and Winston hops 4 meters per second. Eventually, Winston will overtake Tina. How long will that take? How far will Winston have to hop? It will take ___ seconds for Winston to hop ___ meters and catch up to Tina.

It will take Winston 11 seconds to hop 44 meters and catch up to Tina

Step-by-step explanation:

Set up an equation where x represents the number of seconds:

Tina will be represented by s + 33 since she goes 1 m/sec and she has a 33 meter head start, and Winston will be 4s. We need to find when Winston will catch up, so we need an equal sign.

s + 33 = 4s

Solve for s:

s + 33 = 4s

33 = 3s

11 = s

= 11 seconds

Then, plug in 11 as s to find how many meters he will go:

s + 33

11 + 33 = 44

= 44 meters

∠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.

c is the answer

step-by-step explanation: