When traveling with the current, it takes Kamal 1 hour to travel 12 miles on a boat. It takes the boat 1.5 hours to travel the same 12 miles when traveling against the current. Assuming the boat travels at a constant speed during both trips, what is the speed of the boat and the speed of the current?

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

Step-by-step explanation:

r = rate of boat (speed of boat)

t = time

d = distance.

c = rate of current (speed of current)

with the current, the formula becomes (r + c) * t = d

against the current, the formula becomes (r - c) * t = d

going with the current, the boat takes 1 hour to travel 12 miles.

therefore:

(r + c) * t = d becomes (r + c) * 1 = 12

going against the current, the boat takes 1.5 hour to travel the same 12 miles.

therefore:

(r - c) * t = d becomes (r - c) * 1.5 = 12.

your two equations that need to be solved simultancously are:

(r + c) * 1 = 12

(r - c) * 1.5 = 12

divide both sides of the second equation by 1.5 and leave the first equaion as is to get:

r + c = 12

r - c = 8

add the equations together to get:

2 * r = 20

solve for r to get:

r = 20 / 2 = 10

(r + c) * 1 = 12 becomes (10 + c) * 1 = 12

simplify to get 10 + c = 12

solve for c to get c = 12 - 10 = 2

(r - c) * 1 = 8 becomes (10 - c) * 1 = 8

simplify to get 10 - c = 8

solve for c to get c = 10 - 8 = 2

you have:

r = 10

c = 2

that's your solution.

the rate / speed of the boat is 10 miles per hour.

the rate / speed of the current is 2 miles per hour.

answer: a. 74

step-by-step explanation:

it shows divided evenly, so add the 37+37 = 74

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.