To solve this problem, we can use the concept of speed, distance, and time. The relationship between these quantities is given by the formula:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Let the speed of bus B be $x$ km/h. Then, the speed of bus A will be $x + 10$ km/h because bus A is 10 km/h faster than bus B.

Step 1: Write the time equation for both buses

Since both buses travel for the same amount of time, we can set up an equation based on the time taken by each bus. The time taken by each bus can be expressed as:

$\text{Time for bus A} = \frac{120}{x + 10}$ $\text{Time for bus B} = \frac{80}{x}$

Since the times are equal, we set the two expressions equal to each other:

$\frac{120}{x + 10} = \frac{80}{x}$

Step 2: Solve the equation

To solve for $x$, cross-multiply:

$120x = 80(x + 10)$

Expand and simplify the equation:

$120x = 80x + 800$

Subtract $80x$ from both sides:

$40x = 800$

Divide both sides by 40:

$x = 20$

Step 3: Determine the speeds

• The speed of bus B is $x = 20$ km/h.
• The speed of bus A is $x + 10 = 30$ km/h.

Final Answer:

• The speed of bus B is 20 km/h.
• The speed of bus A is 30 km/h.

Would you like to see the detailed steps or have any questions? Here are some related questions to explore:

1. What would be the time taken by each bus to travel their respective distances?
2. How would the equation change if bus A was 15 km/h faster than bus B?
3. What if both buses traveled the same distance instead?
4. How would the problem change if the distances were given in miles instead of kilometers?
5. What would be the speed of each bus if the time for each was given?

Tip: When dealing with distance, speed, and time problems, always set up your equations based on the relationship $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ and identify the known and unknown quantities clearly.