62 Algebra. 



lo. The total area of two squares is a square feet. A side 

 of one square is found to differ from a side of the other by d feet. 

 Find the side of each square. 



Is this problem possible for all values of a'? 



//. Two trains are dispatched from a station, one starting an 

 hour before the other. The rate of motion of the later train is 5 

 miles per hour more than that of the other, and it overtakes the 

 first train at a distance of 150 miles from the station. Find the 

 rate of motion of each train. 



12. Generalize the foregoing problem and solve it. Discuss 

 the results. 



13. A rectangular metal plate is 20 inches longer than wide. 

 It is expanded by heat until each dimension increases by ^ir ^^ its 

 former length, thereby increasing the area of the plate 246 square 

 inches. Find the original dimensions of the plate. 



14.. A man, born in 1806, died at the age of x in the j-ear 

 x^. When did he die ? 



75. Two trains pass at a junction. One is traveling south at 

 the rate of 30 miles an hour and the other is traveling west at the 

 rate of 40 miles per hour. How long before the two trains are 

 100 miles apart? 



Interpret the two results. 

 16. Tw^o trains, A and B, are traveling on roads at right 

 angles to each other, each approaching the crossing. A is 10 

 miles from the crossing and traveling uniformly 30 miles an 

 hour, while at the same instant B is 20 miles from the crossing 

 and traveling uniformly 40 miles an hour. When will they be 5 

 miles apart ? 



Explain the two results. 

 ij. Two trains, A and ^9, 'are traveling on roads at right 

 angles to each other. A is \\o miles from the crossing and 

 is moving towards it at the ['uniform rate of 30 miles an hour. 

 B is 20 miles from the crossing and is moving from it at the uni- 

 form rate of 25 miles an hour. At what times are the trains 90 

 miles apart ? 



Interpret the results. 



