# Ships

Red ship begins its circuit every 30 minutes. Blue boat begins its circuit every 45 minutes. Both ships begin their sightseeing circuit in the same place at the same time always at 10:00 o'clock.

a / What time does meet boat again?
b / How many times a day sail from a port at the same time when at 19:00 o'clock both ships end?

Result

a = 11:30 h
b =  6

#### Solution:

$45 = 3 \cdot 3 \cdot 5 \ \\ 30 = 2 \cdot 3 \cdot 5 \ \\ \ \\ \text{LCM}(45, 30) = 90 \ \\ a = 10 + 90/60 = 11.5 = 11:30 \ \text{h}$
$b = (19-10)/(90/60) = 9/1.5 = 6$

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