DISTANCE WORD PROBLEMS WITH SOLUTIONS
About "Distance word problems with solutions"
Distance word problems with solutions :
We can solve many real world problems using the distance between points on a grid.
Distance word problems with solutions - Examples
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.
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