How to set up problem and solve?

Question

The speed of the current in a river is 2 Kilometers per mile. Bob kayaks 24 kilometers upstream then 24 kilometers downstream in a total of 5 hours. What is bobs speed if there is no currenr

Answer 1

let X = Actual speed 

 

Effective speed downstream = X+2 :  as speed of river is 2 km/hr  ( I assume there is a correction in units)

 

Effective speed upstream = X-2

 

Let time taken for down stream = t₁ 

and upstream = t₂

 

t₁ +t₂ = 5  (time in hours)  given

 

Speed = distance /time

 

X+2 = 24 /t₁  Gives t₁ = 24/(X+2) and t₂ = 24/ (X-2)

 

These equations give 24/(X+2) + 24/(X-2) = 5

Which gives equation as 5X² -48X -20=0 

or 5X² -50X +2X -20=0

Gives X = 10 km/hr and -2/5 km/hr . -2/5 km/hr can be ignored

 

Actual Speed  =10km/hr