rate distance and time

Question

A motorboat takes
4
hours to travel
128km
going upstream. The return trip takes
2
hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

v = speed in still water

w = speed of current

 

Upstream trip:

 

t₁ = 4 hours, d = 128 km

 

(v - w)t₁ = d

 

(v - w)(4) = 128 ⇒ v - w = 32

 

Downstream:

 

t₂ = 2 hours, d = 128 km

 

(v + w)(2) = 128 ⇒ v + w = 64

 

You need to solve a system of 2 equations in two unknowns v and w:

 

v - w = 32

v + w = 64

 

Add the two equations and get 2v = 96 ⇒ v = 48 km/hour

 

Substitute v = 48 into either equation to find w.  From the top equation,

 

48 - w = 32 ⇒ w = 16 km/hour