The hikers plan to visit a scenic lookout. they will rest after they hike 2 miles. then they will hike the remaining 1 3/4 miles to the lookout. the trail the hikers will use to return from the lookout is 1/2 mile shorter than the trail they will use to go to the lookout. each hiker will bring 1/4 gallon of water for each mile to and from the lookout. determine the total distance, in miles, each hiker will hike? and determine the total number of gallons of water each hiker will bring ?

Step-by-step explanation:

The distance to the lookout is the sum of distances before and after the rest stop:

... "to" distance = 2 mi + 1 3/4 mi = 3 3/4 mi

The distance from the lookout is 1/2 mile shorter, so is ...

... "from" distance = 3 3/4 mi - 2/4 mi = 3 1/4 mi

Then the total hike is ...

... total distance = "to" distance + "from" distance

... = 3 3/4 mi + 3 1/4 mi = 6 4/4 mi

... total distance = 7 mi

The water each hiker will bring is ...

... (7 mi) × (1/4 gal/mi) = 7/4 gal = 1 3/4 gal

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.