2 linear equations with 2 unknowns

Question

My question is "It takes a boat 2 hours to travel 20 miles down a river and 3 hours to return up stream to its starting point. What is the speed of the boat? What is the rate of the river current?"

Answer 1

d = rt, so r = d/t

 

20/2 = 10

20/3 = 6 2/3

 

The rate of the river current adds to or subtracts from the speed of the boat. If I normally row 3 mph but go upstream in a 5 mph current, I'm going backward 2 mph.

 

b + c = 10

b - c = 6 2/3

 

Adding rhe equations together...

 

2b = 16 2/3

b = 8 1/3

 

8 1/3 + c = 10

c = 1 2/3

 

The boat travels 8 1/3 mph in still water and the current rate is 1 2/3 mph.