for the Olympic Dhiraj wants to participate in a 200m race.he can currently run that distance in 51 second and with each day of practice it takes him 2 seconds less. the qualifier for 200m is 31 second . how many days practice will he need to achieve his goal? I want in how many days can he achieve his goal?
Answers
Given: For the Olympics, Dhiraj wants to participate in a 200m race.He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. The qualifier for 200m is 31 seconds.
To find: Number of days that he should practice to achieve his goal of running 200 m in 31 seconds
Explanation: Time taken by Dhiraj on first day = 51 seconds
Time duration reduced by each passing day= 2 seconds
It means he takes 49 seconds on day 2 , 47 seconds on day 3 and so on.
This becomes an arithmetic progression whose first term is 51 and common difference is -2.
Let the first term be denoted as a, common difference by d.
Let the nth day be the day in which he takes 31 seconds to complete 200 m.
Using formula for AP:
31 = a + (n-1) d
=> 31 = 51 + (n-1) * -2
=> 31-51 = -2 ( n-1)
=> -20 = -2 ( n-1)
=> n-1 = 10
=> n = 11
Therefore, it takes him 11 days of practice to complete 200 m in 31 seconds.