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 $45\,min$.
Please an answer which would really help me is one which uses an approach of a linear equation or some sort of it. Since I am slow at learning I would appreciate an aswer that can explain this step by step. Can someone help with this part?.
The answer is 45 minutes.
The logic is simple.
As per the question
Betty walks 85Mts + 5 Min Break +
Betty walks 85Mts + 5 Min Break +
Betty walks 85Mts + 5 Min Break + ..... = 98 Minutes.
.
Betty speed is 15Mts/Sec
85Mts walking = say X
5 Min break = Say Y
Equation would be X + Y + X + Y + ..... = 98 Minutes
We know that Y = 5 minutes break time
X = Time to cover 85 mts at 15 mts per minute. = 85/15 =5.67 minutes
.
The New equation would be
5.67 + 5 + 5.67 + 5 + 5.67 + 5 +... = 98 minutes
.
If we consider One walking stride and one break as one complete stride, then One stride = 5.67 + 5 = 10.67 minutes
n(10.67) = 98 minutes Say n is the number of such strides in 98 minutes.
n = 98/10.67
n = 9.18
We have 9 full strides and 0.18 part of 10th stride 9 full strides have 9 full breaks which would be 45 minutes. (9 * 5 min breaks)
We know that the 10th stride is ( 5.67 min of walking + 5 min break time) However, we are less than half of 10th stride ( 0.18 ) which means we never entered the break time of betty (of 5 minutes)