A builder has three heaps containing 2160, 2880 and 3600 bricks respectively
MATHEMATICS · Multi-part · CBSE · Mathematics · Real Numbers · Real Numbers
Problem
A builder has three heaps containing 2160, 2880 and 3600 bricks respectively. He wants to arrange all the bricks into identical rectangular piles such that the number of piles is as large as possible and no bricks remain unused. After the piles are formed, three different types of trucks leave the site together at 7:00 a.m. The trucks return to the site every 45 minutes, 60 minutes and 75 minutes respectively.
(i) Determine the greatest possible number of piles that can be formed and the number of bricks in each pile.
(ii) Find the time after 7:00 a.m. when all three types of trucks will next arrive at the site together.
(iii) By the moment of their fourth simultaneous arrival, how many round trips will each type of truck have completed?