08 - Sound of Impact be Heard Before the Report of the Gun

Problem
A bullet is fired at a target 1,342 m away. At what point along its path would the sound of the impact of the bullet be heard 1/4 second before the report of the gun, assuming that sound travels at the rate of 335 m/sec and the bullet is 503 m/sec.
 

05 - Sum and Difference of Two Numbers Multiplied to Sum and Difference of Their Squares

Problem
Find two numbers such that their sum multiplied by the sum of their squares is 5500, and their difference multiplied by the difference of their squares is 352.
 

07 - A Man Covers an Unknown Distance at Different Rates

Problem
A man covers the distance A to B in 5 hours and 30 minutes. During the second half of the distance he traveled 1/2 kilometer less per hour than during the first half. In the return trip from B to A, by traveling 1 km/hr faster than during the first half of his trip from A to B, he consumed 3-3/4 hours. Determine the distance AB.
 

Numbers 4, 2, 5, and 18 are Added Respectively to the First Four Terms of AP, Forming Into a GP

Problem
If 4, 2, 5, and 18 are added respectively to the first four terms of an arithmetic progression, the resulting series is a geometric progression. What is the common difference of the arithmetic progression?
 

06 - The Battleship Was Brought to Full Stop After 1 Hour of Voyage

Problem
A battleship started on a 500-mile voyage but was brought to full stop an hour after starting for military reasons, delaying it for full hour, after which it was ordered to proceed at a reduced velocity equivalent to 75% of its former rate. The ship arrived at its destination 3 hours and 3 quarters after scheduled time. If it was desired for the ship to arrive one hour and a quarter sooner, how far from the destination should the ship have been ordered stopped?
 

04 - In a Mixed Company of ASEAN Nationalities

Problem
In a mixed company of Malaysians, Vietnamese, Singaporeans, Thais, and Filipinos, the Malaysians are one less than 1/3 of the Filipinos; and three less than half the Vietnamese. The Filipinos and Thais outnumber the Singaporeans and Vietnamese by 3. The Singaporeans and Filipinos form one less than half the company, and the Singaporeans and Vietnamese form 7/16 of the company. How many persons of each nationality were there?
 

Angle Between Two Zero-Based Vectors in XY-Plane

Problem
What is the angle between zero-based vectors ${\bf V_1} = (-\sqrt{3}, ~ 1)$ and ${\bf V_2} = (2\sqrt{3}, ~ 2)$ in an x-y coordinate system?

A.   0° C.   150°
B.   180° D.   120°

 

Probability of Winning the Carnival Game of Tossing a Coin Into a Table

Problem
In a common carnival game, a player tosses a penny from a distance of about 5 feet onto the surface of a table ruled in 1-inch squares. If the penny (3/4 inch in diameter) falls entirely inside a square, the player receives 5 cents but does not get his penny back; otherwise he loses his penny. If the penny lands on the table, what is his chance to win?

A.   5/16 C.   9/256
B.   1/16 D.   3/128

 

Four Trapezia Formed by the Difference of Two Concentric Squares

Problem
ABCD is a square of side 10 cm. PQRS is a square inside ABCD. PQBA, QRCB, RSDC, and SPAD are identical trapezia, each of area 16 cm2. What is the height of each trapezium if PQ is parallel to AB and SR is parallel to DC?

A.   3 cm C.   2 cm
B.   1.8 cm D.   1.2 cm

 

2016-nov-math-trapezia_3d.jpg

 

Example 04 | Age Related Problem in Algebra

Problem
Albert is as old as Bryan will be when Albert is twice as old as Bryan was when Albert's age was half the sum of their present ages. Bryan is as old as Albert was when Bryan was half the age he will be ten years from now. How old are Albert and Bryan?
 

albert-and-bryan.jpg

 

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