How do you solve the following:?

Question

A family makes a 43.25 km trip in 5.5 hours. On the first part of the trip they crossed a lake in a canoe paddling at 12 km/h. For the rest of the trip, they hiked on a scenic trail. If their average walking speed was 5 km/h, how far did they walk?: *
A. 2.25 km
B..25 km
C. 11.25 km
D. 16.25 km

Answer 1

distance = speed*time
43.25 km = speed*5.5 hours
speed = 7.86 km per hour, this is the average speed for the trip
12km/h * time + 5km/h * time = 43.25 km
(12km/h * time + 5km/h * time)/5.5 hours = 7.68km/h
We have simultaneous equations and can solve for two variables
12x + 5y = 43.25
x + y = 5.5
x = 5.5 - y
Use substitution
12(5.5 - y) + 5y = 43.25
66 - 12y + 5y = 43.25
y = 3.25 hours
That is how long they walked. Multiply this by their average walking speed, 5km/h, to get the answer
3.25hours*5km/hour = 16.25 km
Answer D is correct

Answer 2

let x = paddling distance
43.25 - x = walking distance.

x/12 = paddling time
(43.25-x)/5= walking time
add both times to get 5.5
x/12 + (43.25-x)/5 = 5.5

5x + 12(43.25-x) = 330
5x+519-12x = 330
-7x= -189

x=27 km on water

43.25 - 27 = 16.25 km on ground walking

Answer D is correct