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Xin has been given a 14 day training schedule by her coach - Edexcel - A-Level Maths Pure - Question 2 - 2014 - Paper 2
Question 2
Xin has been given a 14 day training schedule by her coach. Xin will run for A minutes on day 1, where A is a constant. She will then increase her running time by (d... show full transcript
Worked Solution & Example Answer:Xin has been given a 14 day training schedule by her coach - Edexcel - A-Level Maths Pure - Question 2 - 2014 - Paper 2
Step 1
Show that on day 14, Xin will run for (4 + 13d + 13) minutes:
Answer
On day 1, Xin runs for A minutes. Each subsequent day, she increases her running time by (d + 1) minutes.
The total number of days is 14, so by day 14, her running time can be expressed as follows:
a_{n} = A + (n-1)(d + 1)
Substituting n = 14:
a_{14} = A + (14 - 1)(d + 1) = A + 13(d + 1) = A + 13d + 13.
Thus, on day 14, Xin will run for (4 + 13d + 13) minutes.
Step 2
find the value of d.
Answer
On day 1, Yi runs for (4 - 13) minutes, which is -9 minutes. This is not realistic for running times. Thus, it's best to interpret this in terms of daily increments.
Yi's time can be expressed as:
a_{14} = (4 - 13) + 13(2d - 1)
Setting this equal to Xin's time:
a_{14} = A + 13d + 13.
Equating both expressions gives:
a + 13d + 13 = -9 + 13(2d - 1).
Solving this equation should yield the value for d.
Step 3
find the value of A.
Answer
The total running time for Xin over 14 days is 784 minutes. Using the sum formula:
total = 14A + (n-1)(d + 1) imes n / 2 = 14A + (13)(d + 1)
Setting this equal to 784:
14A + 13(d + 1) = 784.
From previously found d, substituting into the equation will allow us to isolate A and solve for its value.