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# systems of equations algebra help?

http://i.imgur.com/1e6o3m7.png

A Mississippi riverboat can travel 30 kilometers downstream in 3 hours and can make the return trip in 5 hours. Find the speed of the boat in still water.

Could use some help with this!

Thanks!

### 1 Answer

- DambarudharLv 77 years agoFavorite Answer
Speed of the boat in still water = u kph

Speed of the water current = v kph

Distance traveled = d = 30 km

Time taken to travel downstream = t1 = 3 hr

Time taken to travel upstream = t2 = 5 hr

We have the following equations :

Downstream : (u + v)t1 = d

=> (u + v)*3 = 30

=> u + v = 30/3 = 10 -------- (1)

Upstream : (u - v)t2 = d

=> (u - v)*5 = 30

=> u - v = 30/5 = 6 ------- (2)

Adding (1) and (2), we have : 2u = 16

=> u = 16/2 = 8

=> Speed of the boat in still water = 8 kph ----- Answer

=> Speed of the water current = 2 kph