Aship travels 62.5 km in 1st hour of sailing. starting from 2nd hour, the distance travelled per hour is x% of that in the preceding hour. it is given that the distance travelled in 4th hour is 32km. a)find value of x. b)find the total distance travelled by the ship in first 6 hours

Speed of the ship in the second hour =  (62.5 * x ) / 100  kph.

In third hour it is  [(62 * x) / 100 ] * x/100]

is 4th hour its is the above * x/100 again  so we can now form the equation

62.5x      x          x
*    *      =  32
100      100      100

62,5 x^3 = 32,000,000
x^3 =  512,000
x = 80 <  Answer  to (a)

(b)  Ship travels 62.5 in first hour then  this falls by a common ratio of 0.8 each hour so we have a geometric sequence 

Dist travelled in 6 hours  =  a1  1 - r^n
                                                 = 62.5* (1 - 0.8^6) / 1 -0.8 = 230.56

                                               1 - r

Answer is    230.56 km 

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