49. Three persons, A, B, and C, engage to build a certain piece of wall for $244.16. While A can build 10 rods, B can build but 6, and C but 41. When the wall is half completed, C ceases to labor upon it, and A and B finish it. What part of the $244.16 ought each to receive? A ought to have $135.85.

SA

Ans. B

C

50. A and B together can build a wall in 4 days, A and C can together build it in 5 days, B and C can together build it in 6 days. What time would it require for all together to accomplish it?

A and B can in one day build of it=11⁄2 of it.

The sum of these fractions, 5+18+18=37, is evidently twice the fractional part accomplished by all in one day. Hence, they all would in one day accomplish ; consequently, in 1-3 days, they would

finish it.

of

50. A note of $10000 given Jan. 1st, 1840, has received the following indorsements: January 1st, 1841, indorsed $2952-28, January 1st, 1842, indorsed $2952-28, January 1st, 1843, indorsed $2952.28. How much remained due January 1st, 1844, interest being computed at 7 per cent.? Ans. There was due $2952.28.

51. Two hunters, A and B, kill a deer, whose weight they are desirous of knowing. For this purpose, they rest a stick across the limb of a tree; then suspending the deer at the shorter extremity, they find that its weight is just counterpoised by the weight of A, who suspends himself by his hands at the other extremity. Without changing

1

the point of support of the stick, they take the deer from the shorter extremity and suspend it at the longer extremity of the stick, when it was found to be exactly balanced oy B's weight, when suspended at the shorter extremity of the stick. Now, supposing A to weigh 147 pounds, and B to weigh 192 pounds, what must have been the weight of the deer?

By the principle of the lever, we know that when different weights at its extremities balance each other, they are to each other inversely as the lengths of the arms to which they are attached. Hence, in the first experiment, we know that the weight of A is to the deer's weight, as the shorter arm is to the longer arm. In the second experiment, the deer's weight is to B's weight, as the shorter arm is to the longer arm. Consequently, A's weight is to the deer's weight, as the deer's weight is to B's weight; that is, the deer's weight is a mean proportional between A's weight and B's weight. Therefore, if we multiply the number of pounds which A weighed, by the number of pounds which B weighed, and extract the square root of the product, it will give the weight of the deer in pounds.

147 × 192=28224.

√28224-168 the weight of the deer in pounds.