MATHalino

Problem
Runners A and B start together in a race around a 900-ft oval track. Runner A is making a speed of 27 ft/sec and runner B at 22.5 ft/sec. How long will it take runner A to be exactly one circumference ahead of runner B.
 

Problem
A tour bus has 80 seats. Experience shows that when a tour costs P28,000, all seats on the bus will be sold. For each additional P1,000 charged, however, 2 fewer seats will be sold. Find the largest possible revenue.
A. P29,000
B. P28,500
C. P28,900
D. P28,700
 

Situation
In the figure shown, each plank carries a uniform load of 100 N/m throughout its length. The supports are on the same plane.
 

1. Find the reaction at A.
   A. 900 N
   B. 800 N
   C. 1400 N
   D. 2400 N
    
2. Find the reaction at B.
   A. 900 N
   B. 800 N
   C. 1400 N
   D. 2400 N
    
3. Find the reaction at C.
   A. 900 N
   B. 800 N
   C. 1400 N
   D. 2400 N
    

Situation
A reinforced concrete slab in the shape of an isosceles trapezoid weighs 3600 N/m². It is supported on the three points as shown in the figure.
 

1. Find the reaction at A.
   A.   16,848 N
   B.   6,716 N
   C.   13,372 N
   D.   2,010 N
2. Find the reaction at B.
   A.   16,848 N
   B.   6,716 N
   C.   13,372 N
   D.   2,010 N
3. Find the reaction at C.
   A.   16,848 N
   B.   6,716 N
   C.   13,372 N
   D.   2,010 N

A gutter whose cross-section is trapezoidal is to be made of galvanized iron sheet of 24 m wide. If its carrying capacity is maximum, find the dimension of the base.
A.   4 m
B.   6 m
C.   8 m
D.   10 m
 

Definition of a Locus
Locus is a Latin word which means "place". In mathematics, locus is the set of points that satisfies the same geometrical properties. In most cases, the relationship of these points is defined according to their position in rectangular coordinates.
 

Example 1
Determine the equation of the curve such that the sum of the distances of any point of the curve from two points whose coordinates are (-3, 0) and (3, 0) is always equal to 8.
    A.   4x² + 49y² - 343 = 0
    B.   7x² + 16y² - 112 = 0
    C.   7x² - 16y² + 112 = 0
    D.   4x² - 49y² + 343 = 0
 

Problem
A man can row 77 km and back in 14 hours. If he can row 6.5 km with the stream at the same time as 4.8 km against the stream, find the rate of the stream.
 

Problem
A car leaves city A for city B, 40 km distant, traveling 50 kph. Thirty minutes later, another car leaves city B for city A at 40 kph. At what point of their path will the first car pass 6 minutes before the second car?
 

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.
 

Problem
In a class experiment, a student needs 5 liters of 6% solution. He found a 4% and a 10% solution in the laboratory. How many liters of each solution should he mix in order to obtain 5 liters of 6% solution?
A. 3.33 liters of 4% and 1.67 liters of 10% solution
B. 1.67 liters of 4% and 3.33 liters of 10% solution
C. 3.67 liters of 4% and 1.33 liters of 10% solution
D. 1.33 liters of 4% and 3.67 liters of 10% solution