Wind and Water Current Problem

Question

A powerboat has a four-hour supply of gasoline. How far can this boat travel from the marina if the rate out against the current is 40km/h and the rate back in with the current is 60km/h?

Answer 1

Let T1 = time travelled out

Let T2 = time travelled in 

 

Four-hour supply  ==>  T1 + T2 = 4 at maximum

 

The distance travelled out is given by D1 = 40*T1

The distance travelled  in  is given by D2 = 60*T2 

 

These distances are the same so 40*T1 = 60*T2

 

Solve the last equation for T1:  T1 = 1.5*T2

 

Plug this in to the first equation:  

 

1.5*T2 + T2 = 4

2.5*T2 = 4

T2 = 4/2.5 = 1.6 hours 

 

Therefore D2 = 60*1.6 = 96 kilometers is how far the boat can travel from the marina 

 

Check:  T1 = 4 - 1.6 = 2.4 hours

            D1 = 40*2.4 = 96 kilometers out