A Real-Life Problem in Speed and Distance: Bus Travel Time Calculation

In this article, we discuss a problem involving a bus traveling a certain distance at two different speed intervals. By breaking down the problem step-by-step, we will show how to calculate the amount of time the bus travels at a higher speed based on the total distance and travel duration.

Understanding the Problem

A bus covered a distance of 160 km in a total of 4 hours. It traveled the first part of the journey at 30 km/h and the rest of the journey at 70 km/h. The question is: for how much time did the bus travel at 70 km/h?

Problem Breakdown and Solution

To solve this, let's denote the time traveled at 30 km/h as ( t_1 ) and the time traveled at 70 km/h as ( t_2 ).

The total distance covered is 160 km. The total time taken is 4 hours.

We can express the total distance in terms of time and speed:

Distance Speed × Time Thus, we have:

30t1 70t2 160 … (1)

From the total time, we get another equation:

t1 t2 4 … (2)

Now, let's substitute ( t_1 4 - t_2 ) from equation (2) into equation (1).

30(4 - t2) 70t2 160

Expanding this, we get:

120 - 30t2 70t2 160

Combining like terms, we get:

120 40t2 160

Isolating ( t_2 ), we have:

40t2 40

t2 1

Therefore, the bus traveled at 70 km/h for 1 hour.

To find ( t_1 ):

t1 4 - t2 4 - 1 3 hours

Therefore, the bus traveled for 1 hour at 70 km/h and 3 hours at 30 km/h.

Additional Problem Solving

Let's consider a similar problem where a bus covered a distance of 160 km in 4 hours, part of the distance at 30 kmph and the remaining distance at 70 kmph. The relation is given as:

3(4 - x) 7 160

Solving for x:

12 - 3x 7 160

67x 148

x 2

Thus, the bus traveled for 2 hours at 70 km/h and 2 hours at 30 km/h.

Here is the step-by-step process:

Express the equation based on the given information. Combine like terms to solve for the variable. Calculate the time for each part of the journey.

Conclusion

Understanding and solving such problems can help improve your ability to comprehend and manipulate real-life scenarios in terms of speed, time, and distance calculations. The key to solving these types of problems is to establish the correct equations and solve them systematically.

Keywords: bus speed calculation, distance and time problem, speed and distance equation