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143 Rh 20. A man agreed to work a days on these conditions: for each day he worked he was to receive c cents, and for each day he was idle he was to forfeit d cents. At the end of a days he received m cents. How many days was he idle ?

21. A sum of money is divided among three persons: the first receives a dollars more than a third of the whole sum; the second receives 6 dollars more than a half of what remains; and the third receives c dollars, the amount which is left. Find the original sum.

22. Out of a certain sum a man paid $96; he loaned half of the remainder, and then spent one-fifth of what he had left. After these deductions he still had one-tenth of the original sum. How much had he at first ?

23. A man moves 12 miles in an hour and a half, rowing with the tide, and requires 4 hours to return, rowing against a tide one-quarter as strong: find the velocity of the stronger tide.

24. A man moves a miles in b hours, rowing with the tide, but requires c hours to return, rowing against a tide d times as strong as the first: find the velocity of the stronger tide.

25. A has a certain sum of money from which he gives to B $4 and one-sixth of what remains; he then gives to C $5 and one-fifth of what remains, and finds that he has given away half of his money. How many dollars had A, and how many dollars did B receive ?

26. The fore-wheel of a carriage is a feet, and the hind-wheel is 6 feet in circumference. What is the distance passed over when the fore-wheel has made c revolutions more than the hind-wheel ?

27. Ina certain weight of gunpowder the nitre composed 10 pounds more than two-thirds of the weight, the sulphur 4$1⁄2$ pounds less than one-sixth, and the charcoal 5$1⁄2$ pounds less than one-fifth of the nitre. What was the weight of the gunpowder ?

28. Two-thirds of A’s money is equal to B’s, and three-fourths of B’s is equal to C’s; together they have $650. What amount has each ?

29. A dealer spends $1450 in buying horses at $100 each and cows at $380 each ; through disease he loses 10 per cent of the horses and 20 per cent of the cows. By selling the remainder at the price he gave for them he receives $1260: find how many of each kind he bought.

A 30. A, B, C start from the same place at the rates of c, c+d, c+2d miles an hour respectively: B starts k hours after A; how long after B must C start in order that they may overtake A at the same instant, and how far will they then have walked?