Question

Explain step by step

Answer 1

$\bold{Let\;the\;Total\;Distance\;of\;the\;Marathon\;be : D}$

Given : The First Runner Finds a Water Station after Covering $(\frac{1}{7})th$ of the Total Distance.

The First Runner Finds a Water Station after Covering a Distance of $: \bold({\frac{D}{7})}$

Given : The First Runner gets a Medical Aid after Covering $(\frac{1}{6})th$ of the Total Distance.

The First Runner gets a Medical Aid after Covering a Distance of $: \bold({\frac{D}{6})}$

Given : Another Runner joins the First Runner 4 km after the Medical Aid Station

The First Runner Joins the Second Runner after Covering a Distance of $\bold{: (\frac{D}{7} + \frac{D}{6} + 4)\;km}$

Given : The Second Runner stops 4 km before the Completion of Run, Covering $(\frac{1}{2})th$ of the Total Distance.

The Second Runner Covers a Distance of $: \bold({\frac{D}{2})}$ and Stops 4 km before the Completion of Run.

We can Notice that : The Distance covered by the First Runner before joining the Second Runner + The Distance covered by the Second Runner + 4 km gives us the Total Distance

$\bold{\implies Total\;Distance = [\frac{D}{7} + \frac{D}{6} + 4 + \frac{D}{2} + 4]}$

$\bold{\implies D = [\frac{D}{7} + (\frac{D + 3D}{6}) + 8]}$

$\bold{\implies D = [\frac{D}{7} + (\frac{4D}{6}) + 8]}$

$\bold{\implies D = [\frac{D}{7} + (\frac{2D}{3}) + 8]}$

$\bold{\implies D = [(\frac{3D + 14D}{21}) + 8]}$

$\bold{\implies D = [(\frac{17D}{21}) + 8]}$

$\bold{\implies (D -\frac{17D}{21}) = 8}$

$\bold{\implies (\frac{21D - 17D}{21}) = 8}$

$\bold{\implies (\frac{4D}{21}) = 8}$

$\bold{\implies (\frac{D}{21}) = 2}$

$\bold{\implies D = 42}$

$\bold{The\;Total\;Distance\;of\;the\;Marathon\;is : 42\;km}$