How do I find the time a person has rested when it makes succesive stops?

Jun 2017
399
6
Lima, Peru
The problem is as follows:

Betty goes out from her home for a stroll in the park. We know that she takes a rest $5$ minutes each $85\,m$. If she walks with a constant speed of $15\frac{m}{min}$ and she takes $98$ minutes to get back to her home. How long does she took rest?

The alternatives in book are as follows:

$\begin{array}{ll}
1.&\textrm{43 min}\\
2.&\textrm{45 min}\\
3.&\textrm{35 min}\\
4.&\textrm{40 min}\\
\end{array}$

How can I find the time she has rested in this given context?

What I attempted to do is to find the total time of minutes she has rested by adding the resting time and the time she was walked.

Assuming that the length between her home and all the stroll she has made is $x$:

Then this would be:

$x\left(\frac{1\,min}{15\,m}\right)+x\left(\frac{5\,min}{85\,m}\right)=98$

But this didn't result in an answer near to any of the alternatives. What could be wrong? Can someone help me here?
The answer my book states is $45\,min$.
 

skeeter

Math Team
Jul 2011
3,360
1,850
Texas
it takes Betty 17/3 min to walk 85 meters, then she rests 5 min.

one period of (walk+rest) totals 10 and 2/3 minutes.

at most, there are 9 such periods totaling 96 minutes ... which means she walks the last 2 minutes

so, for the 9 periods, she walks a total of 51 min, rests 45 min, then walks the last 2 min
 
Jun 2017
399
6
Lima, Peru
it takes Betty 17/3 min to walk 85 meters, then she rests 5 min.

one period of (walk+rest) totals 10 and 2/3 minutes.

at most, there are 9 such periods totaling 96 minutes ... which means she walks the last 2 minutes

so, for the 9 periods, she walks a total of 51 min, rests 45 min, then walks the last 2 min
This approach seemed more logical than what I've attempted to do. I think the catch was to calculate the total time and divide this to the total time such the remainder of that division will indicate how long has walked in the final stroll.