word problem

Question

A motorboat travels 128 mi in 4 hours going upstream. It travels 192 mi going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current? 

Answer 1

Hello Mya,

Let us start this problem by assigning variables. Let m be the speed of the boat and c be the speed of the current as these are the two factors to contribute to the speed that is perceived. 

Distance = rate x time 

so rate = Distance/time

 

upstream the speed is 128/4=32

downstream the speed is 192/4=48

 

upstream the boat is going against the current and downstream with the current so we end up with two equations

m+c=48 (downstream)

m-c=32 (upstream) 

 

you can solve this system by elimination or substitution. 

 

If you are not sure how to finish from here let me know

Answer 2

v = speed of boat in still water

w = speed of current

 

Upstream:

 

(v-w)(4 hrs) = 128 mi

 

Downstream:

 

(v+w)(4 hrs) = 192 mi

 

Solve system of 2 equations in 2 unknowns v and w:

 

4(v-w) = 128

4(v+w) = 192

 

Add these 2 equations and get v:

 

8v = 320

 

v = 320/8 mi/hr = 40 mi/hr

 

Plug this v into either of the 2 equations and get w (e.g. top equation):

 

4(40-w) = 128

 

w = (40 - 128/4 ) mi/hr = 8 mi/hr