Question

Julie and Eric row their boat (at a constant speed) downstream for 40 miles in 4 hours, helped by the current. Rowing at the same rate the trip back, against the current, takes 10 hours. Find the rate of the current.

Answer 1

Answer: 3 miles per hour

Step-by-step explanation:

Use the formula "distance (d) = rate (r) x time (t)" to create a system of equations.

Let "r" represent the rate they are rowing

Let "c" represent the current

                            time          rate      distance        EQUATION

Downstream:     4 hours     r + c       40 miles         4(r + c) = 40

Upstream:         10 hours    r - c        40 miles         10(r - c) = 40

Distribute, then eliminate r to solve for c:

Down: 4r + 4c = 40  →   5(4r + 4c = 40)  →   20r + 20c = 200

  Up: 10r - 10c = 40  → -2(10r - 10c = 40) → -20r + 20c =  -80

                                                                                40c = 120

                                                                              ÷40    ÷40

                                                                                    c =   3