SOLUTION: Identify the variables, write a system of equations to solve (Problem on my exam study guide) When she rows with the current, Mindy can row 24 miles in 3 hours. Against the same

Question 1009854: Identify the variables, write a system of equations to solve
(Problem on my exam study guide)
When she rows with the current, Mindy can row 24 miles in 3 hours. Against the same current, Mindy can row only ⅔ of this distance in 4 hours. Find the rate of the current and Mindy's rowing rate in still water. Assume that both are constant.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance
let a = the rate of the boat
let b = the rate of the current.

with the current, the rates are additive.
against the current, the rate are subtactive.

going with the current, rate * time becomes:

(a + b) * 3 = 24

going agains the current, rate * time becomes:

(a - b) * 4 = 16

simplify these equations to get:

3a + 3b = 24
4a - 4b = 16

multiply both sides of the first equation by 4 and multiply the second equation by 3 to get:

12a + 12b = 96
12a - 12b = 48

add the equations together to get:

24a = 144

solve for a to get a = 6

your original equations are:

(a + b) * 3 = 24
(a - b) * 4 = 16

replace a in the first equation to get:

(6 + b) * 3 = 24
distribute the multiplication to get:
18 + 3b = 24
subtract 18 from both sides to get:
3b = 6
solve for b to get:
b = 2

you have a = 6 and b = 2
this means the rate of the boat is 6 mph and the rate of the current is 2 mph.

go back to your original equations again and replace a with 6 and b with 2 to get:

(a + b) * 3 = 24 becomes (6+2) * 3 = 24 which becomes 8*3 = 24 which becomes 24 = 24.

(a - b) * 4 = 16 becomes (6-2) * 4 = 16 which becomes 4 * 4 = 16 which becomes 16 = 16.

this confirms the solutions are correct.

the rate of the boat is 6 miles per hour.
the rate of the current is 2 miles per hour.

RELATED QUESTIONS
This is a problem on my Geometry Study guide for the final exam: SR is a diameter of... (answered by MathTherapy)

Write a system of two equations in two variables to solve the problem. How much of a... (answered by mananth)

Word problem as follows:write a system of equationss in two variables. Solve Kathy and... (answered by josmiceli)

I have a problem on my study guide that i'm having trouble. The question is," M(5,3) is... (answered by richwmiller)

My granddaughter is having a problem with the following equation: 3x/2 = 10. I know about (answered by stanbon)

My son has to write a word problem that can be solved using a system of linear equations... (answered by stanbon)

Hi my name is Andrew, and I need help with the following 5 problems my help me with 15... (answered by richard1234)

A lab tech needs to make a 10 liter batch of antiseptic that is 60% alcohol. How can she... (answered by Mathtut)

I have tried multiple times to solve this problem! Please Help and guide me through the (answered by checkley75)