1. ## Word Problem

Samuel is rowing with a constant speed towards a certain place he has marked on his map. With the aid of a current (which has a speed of 2km/h) it takes him only 1 h 20 min to reach his destination. However, on the way back he has to row against the current and it then takes him 4 h to reach his starting point. Find Samuel's speed on the still water.

2. Hello Mr Rayon
Originally Posted by Mr Rayon
Samuel is rowing with a constant speed towards a certain place he has marked on his map. With the aid of a current (which has a speed of 2km/h) it takes him only 1 h 20 min to reach his destination. However, on the way back he has to row against the current and it then takes him 4 h to reach his starting point. Find Samuel's speed on the still water.
Suppose Samuel can row at $\displaystyle x$ km/h in still water. Then his speed when he's rowing with the current is $\displaystyle (x+2)$ km/h, and $\displaystyle (x-2)$ km/h when he's rowing against the current.

So if we now use the formula distance = speed x time, we can find the distance he rows in each direction, and then say they are the same.

1 h 20 min = $\displaystyle 1\tfrac13$ h = $\displaystyle \tfrac43$ h. So on the way out he rows $\displaystyle (x+2)\times \tfrac43$ km. And on the way back he rows $\displaystyle (x-2) \times 4$ km.

So $\displaystyle \tfrac43(x+2) = 4(x-2)$

$\displaystyle \Rightarrow 4(x+2) = 12(x-2)$

$\displaystyle \Rightarrow 4x+8=12x-24$

$\displaystyle \Rightarrow 32 = 8x$

$\displaystyle \Rightarrow x = 4$

So he rows at 4 km/h in still water.