Been stuck on this question for at least an hour, answer ends up being zero.

Question

Question: Will was travelling up a steadily flowing river
(4r was the river’s flow in mph) in a boat fitted
with a constant-speed outboard motor. The
boat’s speed in still water was 4V mph.
He accidentally dropped a bottle overboard.
Fifteen minutes later, he realised his loss,
turned rapidly around, and started back
downstream. He eventually caught up with the
bottle after it had floated downstream for two
miles. How fast was the river flowing?

To figure out how fast the river was flowing, I need to find R. Using some horrific math that is most likely wrong, I found that r = 2, and V = 0, which can't be right as that would be impossible. Can somebody solve this question and hopefully provide an explanation as to how they got there? I've been doing this question for at least an hour. Thanks!

Answer 1

Hi James,

 

River: 4r, Will: 4V

Time taken to realize missing bottle, t1 = 15 min (1 hr/60 min) = 1/4 hr

Time taken to catch up with bottle, t2 = 2t1 = 1/2hr

Distance travel by bottle, X= 2 miles

                  4r

River   <--------

                                           

                                    ---------------------------> Will upstream

  Bottle  <----------------O

            <---------------------------------------------- Will downstream

 

Distance traveled by Will going upstream,

Xu= (4V - 4r)t1 =4(V-r)t1

Distance traveled by Will going downstream,

Xd =(4V + 4r)t2 = 4(V + r)2t1 

Distance traveled by Bottle downstream, X = (4r)t1

 

But  X = 2 and X = (4r)t1 

      (4r)t1 = 2

(4r)(1/4) = 2

             r = 2

              Xu + X = Xd

     4(V - r)t1 + 2 = 4(V + r)2t1

4(V - 2)(1/4) + 2 = 4(V + 2)(2*1/4)

           V - 2  + 2 = 2V + 4

                       V = -4 mph

Negative sign means going against current