10 - Messenger Going From Front To Rear Then To Front Of A Marching Army Column

Problem
An army of troops is marching along a road at 5 kph. A messenger on horseback was sent from the front to the rear of the column and returns immediately back. The total time taken being 10 minutes. Assuming the messenger rides at the rate of 10 kph, determine the length of the column.
 

Number of days the project delayed

Problem
A contractor estimates that he could finish a project in 15 days if he has 20 men. At the start, he hired 10 men then after 6 days, 10 more men are added. How many days was the project delayed?

A.   5 C.   6
B.   3 D.   4

 

Answer Key

Example 05 - Simultaneous Non-Linear Equations of Three Unknowns

Problem
Solve for x, y, and z from the following simultaneous equations.
 

$x^2 - yz = 3$   ←   Equation (1)

$y^2 - xz = 4$   ←   Equation (2)

$z^2 - xy = 5$   ←   Equation (3)
 

Solution

Number of Hours for Pipe to Fill the Tank if the Drain is Closed

Problem 1
A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
 

Problem 2
A pipe can fill a tank in 4 hours if the drain is open. The tank is initially empty. If the pipe runs with the drain open for 1 hour and the pipe is then closed, the tank will be emptied in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
 

Answer Key

 

Probability That Exactly 1 is Defective in Getting 2 Cell Phones

Problem
A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects 2 cell phones at random without replacement. What is the probability that exactly 1 is defective?

A.   0.0190 C.   0.0390
B.   0.0490 D.   0.0290

 

Angle Correction for Repeated Measurement

Problem
The following interior angles (in degree) of a triangular traverse were measured with the same precision.
 

Angle Value No. of Measurement
A 41 2
B 77 6
C 63 2

 

What is the most probable value of angle C, in degrees?
 

A.   62.423° C.   62.571°
B.   62.874° D.   62.745°

 

Expected Profit for the Acceptance of Estimate of an Engineering Company

Problem
An engineering company prepares an estimate for a job. The cost of preparing the estimate is Php10,000. The amount of profit over and above the Php10,000 is Php25,000 if their estimate is accepted. The probability that their estimate will be accepted 0.7 and the probability that their estimate will not be accepted is 0.3. What is the expected profit?

A.   Php12,500 C.   Php14,500
B.   Php13,500 D.   Php10,500

 

Rate of Change of Volume of Sand in Conical Shape

Problem
A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.

A.   2π ft/min C.   3π ft/min
B.   4π ft/min D.   5π ft/min

 

Duel of Two 50% Marksmen: Odds in favor of the man who shoots first

Problem
Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first?

A.   1/3 C.   2/3
B.   1/2 D.   1/4

 

Velocity of Separation: How fast is the distance between two cars changing?

Problem
A Toyota Land Cruiser drives east from point A at 30 kph. Another car, Ford Expedition, starting from B at the same time, drives S30°W toward A at 60 kph. B is 30 km from A. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.

A.   70 kph C.   55 kph
B.   80 kph D.   60 kph

 

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