Question

While riding her bike to the ocean and back home 6 times, Kelly timed herself at 48min, 56min, 41min, 49min, 43min, and 59min. She had set a goal of averaging 51 minutes for her rides. How many minutes will she need to spend on her seventh ride to attain her goal?

Answer 1

she needs to spend 61 minutes in her seventh ride

Step-by-step explanation

The average of a set of numbers is simply the sum of the numbers divided by the total number of values in the set.

so

`average=\frac{sum\text{ of the data}}{number\text{ of values}}`

Step 1

so

a)let x represent the time she spent on her seventh ride

hence

`\begin{gathered} sum\text{ of data=48+56+41+49+43+59+x} \\ number\text{ of values=7} \\ average\text{ time=51} \end{gathered}`

b) now, replace and solve for x

`\begin{gathered} average=\frac{sum\text{ of the data}}{number\text{ of values}} \\ 51=(48+56+41+49+43+59+x)/(7) \\ 51=(296+x)/(7) \\ Multiply\text{ both sides by 7} \\ 51*7=(296+x)/(7)*7 \\ 357=296+x \\ subtract\text{ 296 in both sides} \\ 357-296=296+x-296 \\ 61=x \end{gathered}`

therefore, the answer is

she needs to spend 61 minutes in her seventh ride

I hope this helps you