2. kim and lauren were driving to pennsylvania which is 680 miles from them. they are going to complete their trip in 3 days. the distances and average speeds for the first and second days driven are shown below. first day: 3 hours at an average speed of 60 miles per hour. second day: 5 hours at an average speed of 65 miles per hour. if the average speed on the third day is 35 miles per hour, how many more hours will it take for them to reach their destination?

Kim and Lauren have 5 more hours to reach Pennsylvania.

Step-by-step explanation:

Given,

Total distance = 680 miles

We have to find the number of hours taken by them to reach Pennsylvania.

Solution,

For Day 1:

Speed =

Time = 3 hrs

We know that the distance is equal to speed multiplied with time.

So the equation is;

For Day 2:

Speed =

Time = 5 hrs

We know that the distance is equal to speed multiplied with time.

So the equation is;

Now the total distance traveled in two  days is the sum of distance traveled in day 1 and distance traveled in day 2.

Distance traveled in 2 days =

So the remaining distance they have to travel is equal to total distance minus distance traveled in 2 days.

Remaining distance =

Now also given that the speed on day 3 is .

So the time taken to cover the distance is equal to distance divided by speed.

Hence Kim and Lauren have 5 more hours to reach Pennsylvania.

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week