Mrs. chandler, the p. e. teacher, is pairing off students to race against each other. latrell can run 4 yards per second, and christopher can run 6 yards per second. mrs. chandler decides to give latrell a head start of 10 yards since he runs more slowly. once the students start running, christopher will quickly catch up to latrell. how far will christopher have to run?

Christopher is going to need to run 5 seconds to catch up.

Step-by-step explanation:

0 = 2x - 10

0 - 2x = -10

-2x = -10

x = 5

2 5/8 is the final answer! : )

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt