word problem

Question

The boat goes 24 miles upstream in 2 hours. It goes 36 miles down stream also in 2 hrs. What is the speed of the boat in still water and the speed of the current

Answer 1

Distance = rate * time

 

r is the speed of the boat

s is the speed of the current

 

 24 = (r-s)*2  <--- it goes 24 miles in 2 hours going against the current (upstream); current slows down the boat 

 

 36 = (r+s)*2 <--- it goes 36 miles in 2 hours going with the current (downstream); current speeds up the boat

 

 

24 = 2r -  2s

36 = 2r + 2s

 

60 = 4r <--- adds them together

 

r=15

 

24 = 2(15)  - 2s

36 = 2(15) + 2s

 

24 = 30 - 2s

36 = 30 +2s

 

-6 = -2s

 6 =  2s

 

s=3

 

The speed of the boat is 15 mph;

The speed of the current is 6 mph

Answer 2

Let s= speed in mph in still water

let c= speed of current

 

So

 

2s - c = 24. ( boat traveling 2hrs against current 

2s + c= 36. (boat traveling 2 hrs with current 

 

eliminate c by adding the two equations 

 

4s = 60

 

s = 15. ( divide both sides by 4

 

go back to either equation and solve for c

 

2(15) - c = 24

 

30 - c = 24

 

-c = -6

 

c = 6