As part of a weight reduction program, a man designs a monthly exercise program consisting of bicycling, jogging, and swimming. He would like to exercise at most 20 hours, devote at most 7 hours to swimming, and jog for no more than the total number of hours cycling and swimming. The calories burned per hour by bicycling, jogging, and swimming are 200, 596, and 294, respectively. How many hours should be allotted to each activity to maximize the number of calories burned

Jogging = 10 hours

Swimming = 7 hours

Cycling = 3 hours

Step-by-step explanation:

J = Hours jogging

S = Hours swimming

C = Hours cycling

Since jogging is the activity that burns the most calories, we should maximize the number of hours jogging:

Therefore, the man should jog for 10 hours.

Since swimming is the activity that burns the second most calories, we should maximize swimming hours:

In order to maximize the number of calories burn, the man should go jogging for 10 hours, swimming for 7 hours and cycling for 3 hours.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

50 min

step-by-step explanation:

they will be decreasing both their times in half

60 / 2 = 30

40/2 = 20

30 + 20 = 50