word problem

Question

at noon two bicyclists left a bicycle shop, one heading north, and the other east. When the bicyclist heading north had gone ten miles, the distance between the bicyclists was seven miles more than the difference traveled by the bicyclist heading east. what was the difference between the bicyclists at this time?

Answer 1

Recognize that this problem can be illustrated with a right triangle.  You will be using the Pythagorean formula (A²+B²=C²) to solve.  Cyclist traveling north is the vertical leg (A), cyclist traveling east is the horizontal leg (B) and the distance between them is the hypotenuse (C).  You will be solving for C.

 

Let:

A=10............for cyclist traveling north

B=x..............(variable, unknown) for cyclist traveling east

C=(10-x)+7...distance btwn cyclists after cyclist traveling north travels for 

                     10 miles (per problem statement, is difference between

                     cyclists' respective travel distances (10-x) plus 7 miles

                     (+7))

 

Substitute each term into Pythagorean Formula...

10²+x²=((10-x)+7)²

100+x²=(-x+17)²

100+x²=x²-34x+289...simplify (note x² terms will cancel)

      34x=189

         x=5.56 

 

Substitute into your original triangle side assumptions....

A=10 mi...vertical leg

B=5.56 mi...horizontal leg

C=(10-5.56)+7

  =4.44+7

  =11.44 mi...hypotenuse, distance between  cyclists

 

Check....

A²+B²=C²

10²+5.56²=11.44²

100+30.91=130.87

      130.91≈130.87...check√, close enough, your assumptions for the

                                legs of the triangle (cyclists' distances)are correct.