Question 0411

Arithmetic and Geometric Progressions (APs, GPs)
2011 Paper 1 Question 9 Variant

Question

(i)
A company is digging a tunnel. Using machine A,{A,} the distance dug on the first day is 285{285} metres. On each subsequent day, the distance dug is 6{6} metres less than on the previous day. Digging continues daily up to and including the day when a distance of less than 15{15} metres is dug. What is the distance dug on the 15th{15\textrm{th}} day, and what is the total distance dug when drilling is completed?
[6]
(ii)
Using machine B,{B,} the distance dug on the first day is also 285{285} metres. On each subsequent day, the distance dug is 25{\frac{2}{5}} of the distance dug on the previous day. How many days does it take for the distance dug to exceed 95%{95\%} of the theoretical maximum distance?
[4]

Answer