Boat and Stream

Question

A motor boat can travel 30 km upstream and 28km down stream in 7 hour. It can travel 21km upstream and return in 5 hour. find the speed of the boat in the still water and the speed of the stream.

Answer 1

Distance = (Rate)(Time).  So, Time = Distance/(Rate)

 

Let x = speed of boat in still water

     y = speed of current

 

Then, 30 / (x-y) + 28 / (x+y) = 7

 

         21 / (x-y) + 21 / (x+y) = 5

 

Multiply the first equation by 3 and the second equation by -4:

 

          90/(x-y) + 84/(x+y) = 21

 

         -84/(x-y) - 84/(x+y) = -20

 

Add the equations to get 6/(x-y) = 1.  So, x-y = 6.

 

Since x-y = 6 and 30/(x-y) + 28/(x+y) = 7, we have:  30/6 + 28/(x+y) = 7

 

                                                                                           28/(x+y) = 2

 

                                                                                                x+y = 14

 

So, we have the system:  x - y = 6

                                      x + y = 14

 

Add the equations to obtain 2x = 20

 

So, x = 10 km/hr and y = 4 km/hr