## Examples in Arithmetic and Algebra: Collected and Arranged from TheCambridge Mathematical Papers, as Given in the Schools and Several Colleges ; with Answers |

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amount Answer arithmetic means arithmetic progression bushel Cambridge cent combinations common difference containing continued cost cube root decimal digits distance Divide divisible equal expansion expressed Extract the cube Extract the square feet Find the greatest find the number Find the value gain gallons geometrical progression give Given greater greatest common measure guinea half harmonic increased Insert length less London lost lowest terms meets miles an hour minutes Multiply n terms number of terms partial fractions persons places pound prime proportional prove quantities ratio received Reduce Reduce the following remainder rent Required respectively scale sets Shew shilling simple square root starting supposing taken third travelled watch weight whole yards

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Side 104 - ... all the time; and he finds that he can row 2 miles against the stream in the same time that he rows 3 miles with it. Find the time of his going and returning.

Side 116 - B. less by 1 1 chains than the length of the sewer ; the expense of making it amounted to as many pounds per chain, as there were chains in the street leading to A. The sewer, however, being insufficient to carry off the water, an additional drain was made from a point in this street distant 4 chains from the bridge A., which entered the river at the same point with the sewer, and was equally inclined to the river and sewer. Now it was found that a drain down the middle of each street, at the rate...

Side 146 - ... men every day, and at the same time a storm arose which protracted the voyage three weeks; they were, however, just enabled to arrive in port without any diminution in each man's daily allowance of water. Required the time of the passage, and the number of men alive when the vessel reached harbor.

Side 103 - At the review of an army, the troops were drawn up in a solid mass, 40 deep ; when there were just one-fourth as many men in front as there were spectators. Had the depth however been increased by 5, and the spectators drawn up in the mass with the army, the number of men in front would have been 100 fewer than before.

Side 117 - The hold of a vessel partly full of water (which is uniformly increased by a leak) is furnished with two pumps worked by A and B, of whom A takes three strokes to two of B's ; but four of B's throw out as much water as five of A's.

Side 50 - If 20 men can perform a piece of work in 12 days, how many men will accomplish three times as much in one-fifth of the time ? Ans.

Side 105 - ... £5 with spectators at 2s. each, and two persons ascended with him, he should gain | of his outlay. The gas and the weather proving bad, he pays but half the price of inflating, and ascends alone from the enclosure a fourth part full, and loses J of his outlay.

Side 116 - From the middle of a town two streets branched off and crossed a river that ran in a straight course, by two bridges, A. and B. From their junction a sewer, equally inclined to both streets, led to a point in the river at the distance of 6 chains from the bridge A., and a distance from B. less by...

Side 145 - ... 8 days. But on the evening of the sixth day, 100 men were killed in a sally, and afterwards the mortality increased to 10 daily. Supposing the stock of provisions unconsumed at the end of the sixth day to support 6 men for 61 days ; it is required to find how long it would support the garrison, and the number of men alive when the provisions were exhausted.

Side 53 - Now when it is half way over, the wind changing, it sails two miles an hour faster, and reaches Dover sooner than it would have done had the wind not changed, in the proportion of 6 : 7- Required the rates of sailing and the distance between Dover and Calais.