Question 0421

Arithmetic and Geometric Progressions (APs, GPs)

2021 Paper 2 Question 4 Variant

Question

A gym has three training courses: Apex course, Cheetah course and Guerilla course. In each of the programme, members run 10 lengths of a straight running track. Length 1 is done away from the starting point, length 2 towards the starting point, length 3 away from the starting point, and so on.

For the Apex course, the time taken to run the first length is

{45}

seconds and the time taken to run the last length is

{20}

seconds. The times taken for each of the

{10}

lengths are in arithmetic progression.

(a)

Find the total time taken to run

{10}

lengths in the Apex course.

[2]

In the Cheetah course, the time taken to run each of the

{10}

lengths is constant at

{20}

seconds.

In the Guerilla course, the time taken to run the first length is

{20}

seconds and the time taken to run the last length is

{45}

seconds. The times taken for each of the

{10}

lengths are in geometric progression.

Ellie runs

{30}

lengths. She first runs

{10}

lengths at the Apex course, followed by

{10}

lengths at the Cheetah course and finally

{10}

lengths at the Guerilla course.

Each length of the straight running track is

{100 \textrm{ m}.}

(b)

Find Ellie's average speed for her run of

{30}

lengths.

[5]

(c)

Determine whether, exactly

{9}

minutes after she starts to run, Ellie is running away from or towards her starting point.

[2]

Question

Answer