Question 0415

Arithmetic and Geometric Progressions (APs, GPs)

2015 Paper 1 Question 8 Variant

Question

An athlete trains for an upcoming marathon by running

{20 \textrm{ km}}

consisting of

{50}

laps around a circular track of length

{400 \textrm{ m}.}

He aims to complete the distance in between

{1\frac{1}{2} \textrm{ hours}}

and

{1\frac{3}{4} \textrm{ hours}}

inclusive.

(i)

In Version

{A}

of the training programme, he runs the first lap in

{T \textrm{ seconds}}

and each subsequent lap takes

{1 \textrm{ seconds}}

longer than the previous lap. Find the set of value of

{T}

which will enable him to complete the distance within the required time interval.

[4]

(ii)

In Version

{B}

of the training programme, he runs the first lap in

{t \textrm{ seconds}}

and each subsequent lap takes

{2\%}

more than the time for the previous lap. Find the set of value of

{t}

which will enable him to complete the distance within the required time interval.

[4]

(iii)

Assuming he completes the

{20 \textrm{ km}}

run in exactly

{1\frac{1}{2} \textrm{ hours}}

using both training programme, find the difference in his lap times for his

{50\textrm{th}}

laps, giving your answer to the nearest second.

[3]