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Problems involving lengths and Distances

 

 

Example :

The length of a rectangle is 6 units more than its breadth. Its perimeter is 20 units. Find its length and breadth.
 

Solution :

Let the breadth of the rectangles be x units.
Then length = x + 6 units.  
                                    
2 (length + breadth) = perimeter

Since the perimeter is 20 units, 
therefore length + breadth = 10 units.
                                    
Hence x + (x + 6) = 10 or 2x + 6 =10
    ...              2x = 4, or x = 2
Breadth = 2 units;

length = 2 + 6 = 8 units. Length = 8 units.


 

Example :

The distance between two places A and B is 240 km. A motorcyclist starts from A and a pedestrian starts from B at the same time. The speed of the motorcyclist is 15 times that of a pedestrian. Three hours after they start, they meet at a point M. How far is this point from A and B?

Solution :

It is always helpful, if you draw a figure to show your problem.

Total distance is 240 km.


              15 x km/h for 3 h       x km/h for 3h

Let the speed of the pedestrian be x km per hour.

Speed (km per hour)Distance covered in 3 hour(km)Pedestrianx15x × 3 = 45xMotorcyclist15xx × 3 = 3x
 

Total distance = 240 km

Distance covered by Pedestrian + Distance covered by motorcyclist = 240 km

45

x + 3 x = 240

48

x = 240

x = 5

Speed(km per hour)Distance covered (km)Pedestrian55 × 3 = 15 kmMotorcyclist15 × 5 = 7575 × 3 = 225 km.

They will meet at the point M, which is 15 km from B and 225 km from A.


 


 




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