A fireworks company plans a display using four kinds of rockets that are launched at…
MATHEMATICS · Multi-part · CBSE · Mathematics · Real Numbers · Real Numbers
Problem
A fireworks company plans a display using four kinds of rockets that are launched at regular intervals of 28 s, 36 s, 45 s and 60 s respectively. All four types are first fired together at exactly 8:00 p.m. The programme is to continue for 3 hours. The company has in stock 420 rockets of the first type, 540 of the second, 675 of the third and 900 of the fourth.
(i) Calculate the interval after which all four types of rockets will be fired together again.
(ii) Determine how many times in total all four types will be launched together during the 3-hour display.
(iii) The rockets are to be packed into identical cartons, each carton containing the same number of rockets of each type and leaving none unpacked. Find the greatest possible number of cartons and the number of rockets of each type in one carton.