Question

The table given below shows the distances, in kilometers, between four villages of a state. To find the distance between two villages, locate the square where the row for one village and the column for the other village intersect. (a) Compare the distance between Himgaon and Rawalpur to Sonapur and Ramgarh? (b) If you drove from Himgaon to Sonapur and then from Sonapur to Rawalpur, how far would you drive?

Answer 1

Step 1: Find the difference of the distance between Himgaon and Rawalpur to Sonapur and Ramgarh

From the table, we observe that

The distance between Himgaon and Rawalpur $=$$98\frac{3}{4}km$ $=$$\frac{395}{4}km$

The distance between Sonapur and Ramgarh $=$$40\frac{2}{3}km$$=$$\frac{122}{3}km$

Difference of the distance between Himgaon and Rawalpur to Sonapur and Ramgarh,

$=$ $\left(\left(\frac{395}{4}\right)-\left(\frac{122}{3}\right)\right)$

$=$$\left(\frac{1185-488}{12}\right)$

$=$ $\frac{697}{12}$

$=$ $58\frac{1}{2}$

Step 2: Find the total distance that he would drive

From the table,

Distance between Himgaon and Sonapur $=$$100\frac{5}{6}km$$=$ $\frac{605}{6}km$

Distance between Sonapur and Rawalpur $=$ $16\frac{1}{2}km$ $=$$\frac{33}{2}km$

The total distance that he would drive,

$=$ $\frac{605}{6}+\frac{33}{2}$

$=$$\frac{605+99}{6}$

$=$$\frac{704}{6}$

$=$ $\frac{352}{3}$

$=$$117\frac{1}{3}$$km$
Hence, the total distance that he would drive is $117\frac{1}{3}$$km$