13. If the middle term of [3x - (1)/(2[x^(1/2)])]^4 is equal to the fourth term of [2[x^(1/2)] + 1/2x]^7, find the value of x. (_M. I. T._) ~PROBLEMS~ ~Linear Equations, One Unknown~ 1. A train running 30 miles an hour requires 21 minutes longer to go a certain distance than does a train running 36 miles an hour. How great is the distance? (_Cornell._) 2. A man can walk 2-1/2 miles an hour up hill and 3-1/2 miles an hour down hill. He walks 56 miles in 20 hours on a road no part of which is level. How much of it is up hill? (_Yale._) 3. A physician having 100 cubic centimeters of a 6% solution of a certain medicine wishes to dilute it to a 3-1/2% solution. How much water must he add? (A 6% solution contains 6% of medicine and 94% of water.) (_Case._) 4. A clerk earned $504 in a certain number of months. His salary was increased 25%, and he then earned $450 in two months less time than it had previously taken him to earn $504. What was his original salary per month? (_College Entrance Board._) 5. A person who possesses $15,000 employs a part of the money in building a house. He invests one third of the money which remains at 6%, and the other two thirds at 9%, and from these investments he obtains an annual income of $500. What was the cost of the house? (_M. I. T._) 6. Two travelers have together 400 pounds of baggage. One pays $1.20 and the other $1.80 for excess above the weight carried free. If all had belonged to one person, he would have had to pay $4.50. How much baggage is allowed to go free? (_Yale._) 7. A man who can row 4-1/3 miles an hour in still water rows downstream and returns. The rate of the current is 2-1/4 miles per hour, and the time required for the trip is 13 hours. How many hours does he require to return? ~Simultaneous Equations, Two and Three Unknowns~ 1. A manual training student in making a bookcase finds that the distance from the top of the lowest shelf to the under side of the top shelf is 4 ft. 6 in. He desires to put between these four other shelves of inch boards in such a way that the book space will diminish one inch for each shelf from the bottom to the top. What will be the several spaces between the shelves? 2. A quantity of water, sufficient to fill three jars of different sizes, will fill the smallest jar 4 times, or the largest jar twice with 4 gallons to spare, or the second jar three times with 2 gallons to spare. What is the capacity of each jar? (_Case._)