Monthly archive | MATHalino

Problem 11
A train starting at noon, travels north at 40 miles per hour. Another train starting from the same point at 2 PM travels east at 50 miles per hour. Find, to the nearest mile per hour, how fast the two trains are separating at 3 PM.

Read more about 11-12 Two trains; one going to east, and the other is heading north
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Problem 10
A boy on a bike rides north 5 mi, then turns east (Fig. 47). If he rides 10 mi/hr, at what rate does his distance to the starting point S changing 2 hour after he left that point?

Read more about 10 - A boy on a bike
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Problem 08
A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 miles per hour. How fast does the end of his shadow move?

Read more about 08-09 Rate of movement of shadow on the ground
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Problem 06
A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft/sec, find how fast the lower end is moving when it is 16 ft from the wall.

Read more about 06-07 Ladder slides down the wall
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Problem 04
A triangular trough 10 ft long is 4 ft across the top, and 4 ft deep. If water flows in at the rate of 3 ft³/min, find how fast the surface is rising when the water is 6 in deep.

Read more about 04-05 Water flowing into triangular trough
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Problem 03
A rectangular trough is 10 ft long and 3 ft wide. Find how fast the surface rises, if water flows in at the rate of 12 ft³/min.

Read more about 03 Water flowing into rectangular trough
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Problem 01
Water is flowing into a vertical cylindrical tank at the rate of 24 ft³/min. If the radius of the tank is 4 ft, how fast is the surface rising?

Problem 02
Water flows into a vertical cylindrical tank at 12 ft³/min, the surface rises 6 in/min. Find the radius of the tank.

Read more about 01-02 Water flowing into cylindrical tank
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Time Rates
If a quantity x is a function of time t, the time rate of change of x is given by dx/dt.

When two or more quantities, all functions of t, are related by an equation, the relation between their rates of change may be obtained by differentiating both sides of the equation with respect to t.

August 2010

11-12 Two trains; one going to east, and the other is heading north

10 - A boy on a bike

08-09 Rate of movement of shadow on the ground

06-07 Ladder slides down the wall

04-05 Water flowing into triangular trough

03 Water flowing into rectangular trough

01-02 Water flowing into cylindrical tank

Time Rates | Applications

Chapter 3 - Applications

Solution to Problem 675 | Midspan Deflection