Solve these word problems. explain and show how you got your answer.

1.) a duck can fly 2400 m in 10 min with the wind. against the wind, it can fly only two thirds of this distance in 10 min. how fast could the duck fly in still air? what is the rate of the wind?

2.) a salmon swims 100 m in 8 min downstream. upstream, it would take the fish 20 min to swim the same distance. what is the rate of the salmon in still water? what is the rate of the current?

Number 1. So the duck's OWN speed (if flying without any wind) with the wind behind him is: 
 Where x/10 is the wind speed 
The duck's OWN speed (if flying without any wind) with the wind against him is: 
 Where x/10 is the wind speed Remember  
So we have two equations that must equal each other since they both represent the duck's speed. 
 We need to rearrange to find x 

 Add x/10 to both sides and subtract (1600/10 from both sides gives: 

 
so x must be 400/10 which 40 metres per minute. 

Number 2.  let s=salmon and c=current 
upstream __ s-c=100m/20 min __ s-c=5m/min 

downstream __ s+c=100m/8min __ s+c=12.5m/min 

adding the two equations __ s-c+(s+c)=5+12.5 __ 2s=17.5 __ s=8.75m/min 

substituting __ 8.75+c=12.5 __ c=3.75m/min