How many weeks will it be before Jake will be jogging 61 minutes per day?

Question

Jake jogs for 11 minutes each day for the first week. Each week after, he increases the time by 5 minutes per week.

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Answer 1 · 2018-06-07T17:14:42

He should hit 61 minutes of running by the 11th week

If Jake is increasing his jogging time by 5 minutes each week, starting with the second week, we can write this as a function:

#t=11+5(w-1)#

In the above expression, #t# is the jogging time and #w# is the week number. It's written as #w-1# because on the first week, there is no increase.

We can simplify this expression further before solving our problem by distributing the 5 to both terms in the parentheses:

#t=11+5w-5#

#t=6+5w#

Now, its a matter of plugging in the desired amount of time and figuring out the number of weeks:

#61=6+5w#

#61color(red)(-6)=cancel(6)+5wcolor(red)(cancel(-6))#

#55=5w#

#55/color(red)(5)=(cancel(5)w)/color(red)(cancel(5))#

#color(green)(w=11)#