Question

O LINES AND SYSTEMS Solving a distance, rate, time problem using a system of linear... RY III A motorboat travels 141 kilometers in 3 hours going upstream and 873 kilometers in 9 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? Note that the ALEKS graphing calculator can be used to make computations easier. Rate of the boat in still water: ola km 5 х ? Rate of the current: 0 Explanation Check Stv 2020 McG-Education All Rights Reserved. Terms of Use | Privacy ACCED W

Answer 1

Let x = speed of boat in still water
Let y = speed of the current
then
(x-y) = Upstream speed
(x+y) = downstream speed
:
Write a distance equation for each trip; (Distance = time * speed)
:
Upstream trip equation:
3(x - y) = 141
Simplify, divide both sides by 3; resulting in:
x - y = 47
:
Downstream trip equation:
9(x + y) = 873

Simplify, divide both sides by 9: resulting in:
x + y = 97
:
Use these two equations for elimination:
x - y = 47
x + y = 97
--------------adding eliminates y, find x.
2x = 144
x = 144 / 2
x = 72 km/hr in still water
:
Find y using x + y = 86 to find y, substitute 72 for x:
72 + y = 97
y = 97 - 72
y = 25 km/hr is the current;
:
Check our solution in the upstream trip equation
3(72 - 25) =
3 * 47 = 141 km

Hope This Helps!