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

 

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

 

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

 

Simply Supported Beam with Support Added at Midspan to Prevent Excessive Deflection

Situation
A simply supported beam has a span of 12 m. The beam carries a total uniformly distributed load of 21.5 kN/m.
1.   To prevent excessive deflection, a support is added at midspan. Calculate the resulting moment (kN·m) at the added support.

A.   64.5 C.   258.0
B.   96.8 D.   86.0

2.   Calculate the resulting maximum positive moment (kN·m) when a support is added at midspan.

A.   96.75 C.   108.84
B.   54.42 D.   77.40

3.   Calculate the reaction (kN) at the added support.

A.   48.38 C.   161.2
B.   96.75 D.   80.62

 

Limit the Deflection of Cantilever Beam by Applying Force at the Free End

Situation
A cantilever beam, 3.5 m long, carries a concentrated load, P, at mid-length.

Given:
P = 200 kN
Beam Modulus of Elasticity, E = 200 GPa
Beam Moment of Inertia, I = 60.8 × 106 mm4

 

2018-nov-design-cantilever-beam-given.jpg

 

1.   How much is the deflection (mm) at mid-length?

A.   1.84 C.   23.50
B.   29.40 D.   14.70

2.   What force (kN) should be applied at the free end to prevent deflection?

A.   7.8 C.   62.5
B.   41.7 D.   100.0

3.   To limit the deflection at mid-length to 9.5 mm, how much force (kN) should be applied at the free end?

A.   54.1 C.   129.3
B.   76.8 D.   64.7