45. A merchant bought two pieces of cloth, the first at the rate of $4 for 9 yards, and the second at that of $3 for 4 yards; the second piece contained as many times 3 yards as the first contained times 4 yards. He sold each piece at the rate of $5 for 9 yards, and lost $5 by the bargain. How many yards were there in each piece? Ans. 1st, 144; 2d, 108.

46. At what time between 5 and 6 o'clock will the hands of a watch

be together?

Let x no. minutes past 5.

Ans. 27 minutes past 5.

Minute-hand gains of hour-hand 11 five-minute spaces in an hour; it has 5 such spaces to gain.

.. it will take of an hour, or (60) =27 = x.

47. At what time between 7 and 8 o'clock will the hands of a watch be opposite one another?

Let x no. minutes past 7. (See Ex. 46.)

Minute-hand has 1 five-minute space to gain.

Ans. 5 minutes past 7.

.. it will take of an hour, or (60) = 51 = x.

48. At what times between 6 and 7 o'clock will the hands of a clock be at right angles?

Ans. 16, or 49

Let x = no. minutes past 6. (See Ex. 46.)

minutes past 6.

Minute-hand has 3, or 9, five-minute spaces to gain. .. it will take,

or of an hour, or (60), or (60)

=

161, or 49= x.

49. A certain fraction is equal to 3, and if its numerator is increased by 5 and its denominator by 9 it becomes . Find the fraction. Ans. 1.

50. Two laborers are employed at $3 and $5 a day each. The sum of the days they worked was 40. They each received the same sum. How many days was each employed? Ans. $3-man, 25; $5-man, 15.

The numbers in parentheses show the order in which the equations