Zoe and Maria plan to hike at a rate of 3 miles per hour and canoe at a rate of 6 miles per hour. They want to travel no more than 8 hours and cover at least 40 miles in one day. Which system of inequalities models the situation?

h + c ≤ 8

3h + 6c ≥ 40

where h is the number of hiking hours

c is the number of canoeing hours

Step-by-step explanation:

Here, we want to write a system of inequalities;

Let number of hiking hours be h and the number of canoeing hours be c

h + c ≤ 8

Covering at least 40 miles;

Recall;

distance = speed * time

for 3 miles, h hours, we have 3h miles

for 6 miles , c hours , we have 6c

At least 40 miles, inequality will be ;

3h + 6c ≥ 40

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)