Modelling Linear Systems

Question

It took a patrol boat 5 hours to travel 60km up a river against the current, and 3 hours for the return trip with the current. Find the speed of the boat in still water and the speed of the current.

Answer 1

1. Let v (km/h) be the speed of boat in the still water and 

2. w (km/h) be the speed of the current.

 

Then, we are given

1. 5 (h) * (v - w)(km/h) = 60 (km) => 5 * v - 5 * w = 60

2. 3 (h) * (v+w) (km/h) = 60 (km) => 3 * v + 3 * w = 60

 

Solve the above two equations :

I am going to divide the first equation by 5 and the second by 3. Then

3. v - w = 12

4. v + w = 20

 

If we add the two equations then we have

5. 2v + 0w = 32 => v = 16 (km/h)

Using this and one of 3 or 4, 

w = 4 (km/h)

 

 

Hope this helps! 

Answer 2

Let Current speed = C and Boat speed = B.   Ground speed with current is B+C  and without current = B - C

 

B + C = 60km/3hours  = 20

 

B - C = 60kw/5hours = 12

 

If we subtract the bottom equation from the top one, we get  2C = 8 km/hr or C = 4 km/hr. 

If we add the bottom equation to the top equation we get  2B = 32 km/hr or    B = 16 km/hr