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Math Help - Word Problem

  1. #1
    Member Mr Rayon's Avatar
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    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.
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello Mr Rayon
    Quote Originally Posted by Mr Rayon View Post
    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 x km/h in still water. Then his speed when he's rowing with the current is (x+2) km/h, and (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 = 1\tfrac13 h = \tfrac43 h. So on the way out he rows (x+2)\times \tfrac43 km. And on the way back he rows (x-2) \times 4 km.

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

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

    \Rightarrow 4x+8=12x-24

    \Rightarrow 32 = 8x

    \Rightarrow x = 4

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

    Grandad
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