Chapter 4.8, Problem 3P

To determine

To calculate: the time taken by kwan to uphill.

Answer to Problem 3P

Time taken for uphill 1.8 hrs.

Explanation of Solution

Given:

	$\text{speed}\times \text{time = Distance}$
Up	$?$	$?$	$?$
Dawn	$?$	$?$	$?$

Speed of the kwan to uphill= 4 kmph

Speed of the kwan to downhill= 4 kmph

Total time taken for uphill & downhill =3 hours

Calculation:

Let the distance covered for uphill be = $x$

the time taken for uphill = $\frac{x}{4}$ hours

Let the distance covered for downhill be = $x$

the time taken for uphill = $\frac{x}{6}$ hours

total time taken for uphill & down hill

  $\frac{x}{4}+\frac{x}{6}=3$

Now taking LCM we get

  $\begin{array}{l}\frac{x}{4}+\frac{x}{6}=3\\ \frac{3x+2x}{12}=3\\ 3x+2x=36\\ 5x=36\\ x=\frac{36}{5}\\ x=7.2\end{array}$

So, the distance covered for uphill is 7.2 km

Time taken for uphill

  $\begin{array}{l}\frac{x}{4}=\frac{7.2}{4}\\ 1.8\text{ hours}\end{array}$

	$\text{speed}\times \text{time = Distance}$
Up	$4$	$1.8$	$7.2$ km
Dawn	$6$	$1.8$	$10.8$