Quadratic Equations. 63 



18. Along the sides of a right angle two bodies, A and //, 

 move with unifonii velocity. A is a miles from the vertex and 

 moving p miles per hour, while at the same instant B is b miles 

 from the vertex and moving q miles per hour. At what times are 

 the two bodies d miles apart ? 



Show that the result obtained can be used as a formula to 

 solve Prob. 16. 



Show that by giving the proper interpretation to q, as to its 

 positive or negative character, that the formula can be made to 

 solve either Prob. 16 or 17 at will. 



Under what conditions will the bodies 7iever be d miles apart ? 



7p. Two circles, A and B, move with their centers always 

 on the sides of a right angle. A, whose radius is -R feet, is a 

 feet from the vertex and moving uniformly p feet per second. B, 

 whose radius is rfeet, is b feet from the vertex and moving uni- 

 formly q feet per second. At what times are the circles tangent 

 to each other? 



Result : Tangent externally in 



apj^bq± s/(R^rr(p^ + f) + (ap^bqr ^^^.^ 

 ' f-V(f ' seconas. 



Tangent internally in 



apj^ bq^V(R-rr(P^^gn-V(ap^bqr ^^^^^^^^ 



Show that it is possible for them to be tangent externally and 

 not tangent internally. 



Show that it is impossible for the circles to be tangent inter- 

 nally without first being tangent externally. 



Show that the known quantities, may have such values that 

 the two circles will never be tangent at all. 



20. Find the side of an equilateral triangle, knowing that a 

 side exceeds the altitude by d feet. 



