Question

A ship 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

Answer 1

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