Question

On Sunday, Ben goes to a velodrome to train. He cycles the first lap of the track in 25 seconds Each lap Ben cycles takes him 16 seconds longer than the previous lap.

a) Find the time in seconds, Ben takes to cycle his tenth lap 2.
b) Ben cycles his last lap in 55.4 seconds. Find how many laps he has cycled on Sunday .
c) Find the total time in minutes, cycled by Ben on Sunday.

Answer 1

169 seconds

3rd lap

0.923 minutes

Explanation:

To solve this question, we would use formula for arithmetic progression in solving it.

S(n) = a + (n - 1)d

If a = 25 s

n = 10

d = 16

S(n) = 25 + (10 - 1)16

S(n) = 25 + 9 * 16

S(n) = 25 + 144

S(n) = 169

It takes him 169 seconds to cycle his tenth lap

b

If S(n) = 55.4, what is n

55.4 = 25 + (n - 1)16

55.4 - 25 = (n - 1)16

30.4 = (n - 1)16

n - 1 = 30.4/16

n - 1 = 1.9

n = 1.9 + 1

n = 2.9 approximately 3

Therefore, he's on his 3rd lap

c

Total time cycled is dependent on the total cycles he made, and going to question 2, we were told he made 55.4 seconds of cycle

55.4/60 = 0.923 minutes