**Distance word problems with solutions :**

We can solve many real world problems using the distance between points on a grid.

**Example 1 : **

The coordinate plane represents a map. Each grid unit represents 20 miles. A retail company has warehouses at M(−70, 10) and N(50, 10). How long does it take a truck that drives 40 miles per hour to travel from warehouse M to warehouse N ?

**Solution :**

Let us locate the points M(−70, 10) and N(50, 10) on the graph.

**Step 1 :**

Identify the important information.

One warehouse is located at M(−70, 10). The other is at N(50, 10).

A truck drives from M to N at a speed of 40 miles per hour.

**Step 2 :**

Find the distance between M and N by adding the absolute values of the x-coordinates of the points.

Find the time it takes the truck to drive this distance by using this relationship : distance = rate · time.

**Step 3 :**

Add the absolute values of the x-coordinates to find the distance between point M and point N on the grid.

|-70| + |50| = 70 + 50 = 120

The warehouses are 120 miles apart.

The truck drives 120 miles at 40 mi/h. Because 120 = 40(3), it takes the truck 3 hours to travel from M to N.

**Justify and Evaluate :**

We found the sum of the absolute values of the x-coordinates to find the horizontal distance on the grid.

Then we used distance = rate · time to find the time it takes to drive that distance.

**Example 2 :**

The coordinate plane represents a map. Each grid unit represents 20 miles. A retail company has warehouse at and N(50, 10) and a store is located at P(50, -30). How long will it take a truck driving at 50 miles per hour to drive from warehouse N to this store ?

**Solution :**

Let us locate the points N(50, 10) and P(50, -30) on the graph.

**Step 1 :**

Identify the important information.

The warehouse is located at N(50, 10) and the store is located at P(50, -30) and

A truck drives from N to P at a speed of 50 miles per hour.

**Step 2 :**

The line which connects N and P is parallel to y-axis.

Find the distance between N and P by adding the absolute values of the y-coordinates of the points.

Find the time it takes the truck to drive this distance by using this relationship : distance = rate · time.

**Step 3 :**

Add the absolute values of the y-coordinates to find the distance between point N and point P on the grid.

|10| + |-30| = 10 + 30 = 40

The store P and the warehouse N are 40 miles apart.

The truck drives 40 miles at 50 mi/h. Because 40 = 50(0.8), it takes the truck 0.8 hours or 48 minutes to travel from N to P.

(0.8 hrs = 0.8x60 = 48 minutes)

**Justify and Evaluate :**

We found the sum of the absolute values of the y-coordinates to find the vertical distance on the grid.

Then we used distance = rate · time to find the time it takes to drive that distance.

After having gone through the stuff given above, we hope that the students would have understood "Distance word problems with solutions".

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