Word problem question

Question

bill travels upstream at top speed to his favorite fishing spot, a distance of 528 miles in 6 hours returNing, he finds that the trip downstream still at top speed, only takes 5.5 hrs. Find the rate of bills boat and the speed of the current

 

boat rate mph

current rate mph

Answer 1

Let  b = boat rate in MPH

Let  c = water current in MPH

 

From upstream trip:   6(b - c) = 528    (6 hours at the net speed of boat minus current allows him to travel 528 miles) 

              (divide both sides by 6):    b - c = 88   (1)

 

From downstream trip, use the same logic, except this time you add the boat's speed to the current:   5.5(b + c) = 528

  (div both sides by 5.5):   b + c = 96  (2)

               

Notice that if you add eq (1) to eq (2):

                                        b - c = 88

                              +       b + c = 96  

                           -------------------------

                                      2b + 0c  = 184                            

 

Solve for b by dividing both sides by 2:  b = 92 MPH

 

Use   b=92 in (1) or (2) to get    c = 4 MPH   [ another equally valid way to get  c is to follow a similar path you used to find b, except subtract (1) from (2) to get   2c = 8   ==>  c = 4 ]

 

Check answers in (1) and (2) to make sure they make sense (they do).