The indicated value by writing & solving a system of linear equations using D=R*T. Chase and Charlie decided to take a 10 mile canoe trip down the Crow Wing River. To get to their destination it took them 2 hours, but because of the current, it took them 31//3 hours to get home. How fast were they paddling and what was the rate of the current?

Question

The indicated value by writing & solving a system of linear equations using  D=R*T. Chase and Charlie decided to take a 10 mile canoe trip down the Crow Wing River. To get to their destination it took them 2 hours, but because of the current, it took them  31//3 hours to get home. How fast were they paddling and what was the rate of the current?

Bytelearn · Accepted Answer

Identify Variables and Equations:  Identify the variables and set up the equations based on the problem statement. Let p be the paddling speed in miles per hour and c be the current's speed in miles per hour. The total speed downstream is (p + c) and upstream is (p - c). Convert Time to Decimal:  Convert the time for the upstream journey into a decimal for easier calculation. 31/3 hours is approximately 10.33 hours. Rewrite the upstream equation: 10 = (p - c) × 10.33 Simplify Equations:  Simplify both equations to express them in terms of p and c. Equation for downstream: 10 = 2(p + c) 5 = p + c  (Divide both sides by 2)  Equation for upstream: 10 = 10.33(p - c) 0.967 = p - c  (Divide both sides by 10.33) Solve Using Elimination:  Solve the system of equations using substitution or elimination. Here, we'll use elimination. Add the two simplified equations: 5 = p + c 0.967 = p - c ----------------- 5.967 = 2p p = 2.9835 (Divide both sides by 2)

Full solution

More problems from Convert a recursive formula to an explicit formula

Related topics