ENGR. BESAVILLA’S NOTES
Problem 89 Problem 95
A parking lot charges X for the first hour or fraction of an hour and 2/3 X for A circle of radius 1 inch is inscribed in an equilateral triangle. A smaller circle
each hour or fraction thereafter. Smith parks 7 times as long as Jones, but is inscribed at each vertex, tangent to the circle and two sides of the triangle.
pays only 3 times as much. How long did each park? (The time clock The process is continued with progressively smaller circles. What is the sum
registers only in 5-minute intervals). of the circumference of all circles?
Ans: Jones = 0.5 hours Ans: 5π
Smith = 3.5 hours
Problem 96
A man leaves from the point where the prime meridian crosses the equator
Problem 90
and moves forty-five degrees northeast by geographic compass which
Mr. Field,, a speeder, travels on a busy highway having the same rate of
always points toward the north geographic pole. He constantly corrects his
traffic flow in each direction. Except for Mr. Field, the traffic is moving at the
route. Assuming that he walks with equal facility on land and sea, where
legal speed limit. Mr. Field passes one car for every nine which he meets
does he end up and how far will he hav traveled when he gets there?
from the opposite direction. By what percentage is he exceeding the speed
limit? Ans: North Pole, 2 x 10 7 meters
Ans: 25%
Problem 97
Three hares are standing in a triangular field which is exactly 100 yards on
Problem 91
each side. One hare stands at each corner; and simultaneously all three set
The teacher marked the quiz on the following basis: one point for each
off running. Each hare runs after the hare in the adjacent corner on his left,
correct answer, one point off for each question left blank and two points off
thus following a curved course which terminates in the middle of the field, all
for each question answered incorrectly. Pat made four times as many errors
three hares arrriving there together. The hares obviously ran at the same
as Mike, but Mike left nine more questions blank. If they both got the same
speed, but just how far did they run?
score, how many errors did each make?
Ans: Pat = 8 errors Ans: 100 yards
Mike = 2 errors
Problem 98
A scalene triangle ABC which is not a right triangle has sides which are
Problem 92 integers. If sin A = 5/13, find the smallest values for its sides, i.e., those
A student just beginning the study of logarithms was required to evaluate an values which make the perimeter a minimum.
log A Ans: a = 25
expression of the form . He proceeded to cancel common factors in
log B b = 16
both numerator and denominator, (including the “factor” log), and arrived at c = 39
the result 2/3. Surprisingly, this was correct. What were the values of A and
B?
Problem 99
Ans: A = 9/4 A one-acre field in the shape of a right triangle has a post at the midpoint of
B = 27/8 each side. A sheep is tethered to each of the side posts and a goat to the
post on the hypotenuse. The ropes are just long enough to let each animal
reach the two adjacent vertices. What is the total area the two sheep have to
Problem 93 themselves, i.e., the area the goat cannot reach?
A forgetful physicist forgot his watch one day and asked an E.E. on the staff
Ans: one acre
what time it was. The E.E. looked at his watch and said: “The hour, minute,
and sweep second hands are as close to trisecting the face as they ever
come. This happens only twice in every 12 hours, but since you probably Problem 100
haven’t forgotten whether you ate lunch, you should be able to calculate the A divided highway goes under a number of bridges, the arch over each lane
time.” What time was it to the nearest second? being in the form of a semi-ellipse with the height equal to the width. A truck
is 6 ft. wide and 12 ft. high. What is the lowest bridge under which it can
Ans: 2:54:35 pass?
9:05:25
Ans: 13 ft. and 5 inches
Problem 94 Problem 101
A spider and a fly are located at opposite vertices of a room of dimensions 1, A cowboy is five miles south of a stream which flows due east. He is also 8
2 and 3 units. Assuming that the fly is too terrified to move, find the minimum miles west and 6 miles north of his cabin. He wishes to water his horse at the
distance the spider must crawl to reach the fly. stream and return home. What is the shortest distance he can travel and
accomplish this?
Ans: 18
Ans: 17.9 miles
Problem 89 Problem 95
A parking lot charges X for the first hour or fraction of an hour and 2/3 X for A circle of radius 1 inch is inscribed in an equilateral triangle. A smaller circle
each hour or fraction thereafter. Smith parks 7 times as long as Jones, but is inscribed at each vertex, tangent to the circle and two sides of the triangle.
pays only 3 times as much. How long did each park? (The time clock The process is continued with progressively smaller circles. What is the sum
registers only in 5-minute intervals). of the circumference of all circles?
Ans: Jones = 0.5 hours Ans: 5π
Smith = 3.5 hours
Problem 96
A man leaves from the point where the prime meridian crosses the equator
Problem 90
and moves forty-five degrees northeast by geographic compass which
Mr. Field,, a speeder, travels on a busy highway having the same rate of
always points toward the north geographic pole. He constantly corrects his
traffic flow in each direction. Except for Mr. Field, the traffic is moving at the
route. Assuming that he walks with equal facility on land and sea, where
legal speed limit. Mr. Field passes one car for every nine which he meets
does he end up and how far will he hav traveled when he gets there?
from the opposite direction. By what percentage is he exceeding the speed
limit? Ans: North Pole, 2 x 10 7 meters
Ans: 25%
Problem 97
Three hares are standing in a triangular field which is exactly 100 yards on
Problem 91
each side. One hare stands at each corner; and simultaneously all three set
The teacher marked the quiz on the following basis: one point for each
off running. Each hare runs after the hare in the adjacent corner on his left,
correct answer, one point off for each question left blank and two points off
thus following a curved course which terminates in the middle of the field, all
for each question answered incorrectly. Pat made four times as many errors
three hares arrriving there together. The hares obviously ran at the same
as Mike, but Mike left nine more questions blank. If they both got the same
speed, but just how far did they run?
score, how many errors did each make?
Ans: Pat = 8 errors Ans: 100 yards
Mike = 2 errors
Problem 98
A scalene triangle ABC which is not a right triangle has sides which are
Problem 92 integers. If sin A = 5/13, find the smallest values for its sides, i.e., those
A student just beginning the study of logarithms was required to evaluate an values which make the perimeter a minimum.
log A Ans: a = 25
expression of the form . He proceeded to cancel common factors in
log B b = 16
both numerator and denominator, (including the “factor” log), and arrived at c = 39
the result 2/3. Surprisingly, this was correct. What were the values of A and
B?
Problem 99
Ans: A = 9/4 A one-acre field in the shape of a right triangle has a post at the midpoint of
B = 27/8 each side. A sheep is tethered to each of the side posts and a goat to the
post on the hypotenuse. The ropes are just long enough to let each animal
reach the two adjacent vertices. What is the total area the two sheep have to
Problem 93 themselves, i.e., the area the goat cannot reach?
A forgetful physicist forgot his watch one day and asked an E.E. on the staff
Ans: one acre
what time it was. The E.E. looked at his watch and said: “The hour, minute,
and sweep second hands are as close to trisecting the face as they ever
come. This happens only twice in every 12 hours, but since you probably Problem 100
haven’t forgotten whether you ate lunch, you should be able to calculate the A divided highway goes under a number of bridges, the arch over each lane
time.” What time was it to the nearest second? being in the form of a semi-ellipse with the height equal to the width. A truck
is 6 ft. wide and 12 ft. high. What is the lowest bridge under which it can
Ans: 2:54:35 pass?
9:05:25
Ans: 13 ft. and 5 inches
Problem 94 Problem 101
A spider and a fly are located at opposite vertices of a room of dimensions 1, A cowboy is five miles south of a stream which flows due east. He is also 8
2 and 3 units. Assuming that the fly is too terrified to move, find the minimum miles west and 6 miles north of his cabin. He wishes to water his horse at the
distance the spider must crawl to reach the fly. stream and return home. What is the shortest distance he can travel and
accomplish this?
Ans: 18
Ans: 17.9 miles
