# 03 - In rowing a boat: find the rate of stream

**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.

# 02 - Cars moving in opposite directions

**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?

# 01 - Sound of impact of the bullet hitting the target

**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.

# 01 - Example of Mixture Related Problem

**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

# 13 - Length of Belt Connecting Two Pulleys

**Situation**

Two flat belt pulleys have a center to center distance of 137 cm, and diameters of 72 cm and 36 cm, respectively. Neglecting the sagging of belt.

- Compute the length of belt if both pulleys will rotate in the same direction.

A. 464.5 cm

B. 553.1 cm

C. 446.0 cm

D. 535.4 cm

- Compute the length of belt if the belt will be cross-connected to make the pulleys rotate in opposite directions.

A. 654.1 cm

B. 465.2 cm

C. 564.2 cm

D. 645.1 cm

- Determine the distance of the point from the center of the bigger pulley where the belt will cross when cross-connected.

A. 91.3 cm

B. 100.4 cm

C. 89.4 cm

D. 98.7cm

# 04 - Solution of Radical Equation

**Problem 7**

Determine the value of $x$ from $\sqrt[4]{3^{x^2}\sqrt{3^{x - 1}}} = \sqrt[8]{9^{x + 1}}$

# 02 - Solution to Equations Involving Variable Exponent

Solve for the value of x from each of the following equations:

- 9
^{x}- 6(9^{-x}) - 1 = 0 - 2
^{x + 1}· 3^{x}= 5^{x + 3}

# 01 - Solution of Logarithmic Equations

Solve for x from the following:

- $\log_6 (x - 2) + \log_6 (x + 3) = 1$

- $x^{\log x} = 10\,000$

# Example 07 - Simultaneous Non-Linear Equations of Two Unknowns

**Problem**

Solve for $x$ and $y$ from the given system of equations.

$\dfrac{3}{x^2} - \dfrac{4}{y^2} = 2$ ← Equation (1)

$\dfrac{5}{x^2} - \dfrac{3}{y^2} = \dfrac{17}{4}$ ← Equation (2)