Calculating Distance: When Speed and Time are Given
Calculating Distance: When Speed and Time are Given
This article explains the process of calculating the distance covered by Asha to reach her office, using the given speed and time information. It provides step-by-step solutions to similar problems, helping you understand the relationship between speed, time, and distance. The calculations are explained using multiple methods and are structured to meet Google's SEO guidelines.
Understanding the Problem
Asha drives to work at an average speed of 48 km per hour. The time taken to cover the first 60 km of the distance is 10 minutes more than the time taken to cover the remaining distance. We need to determine the total distance to her office.
Problem 1: Method 1
We start by defining the total distance as D km. The time taken to cover the first 60 km is D * 60 / 100 / 48 hours and the time taken for the remaining distance is (D - 60) * 40 / 100 / 48 hours.
The equation derived from the given condition is:
(D * 60 / 100 / 48) - ((D - 60) * 40 / 100 / 48) 10 / 60
Simplifying this, we get:
3D / 5 - 2D / 5 8
Solving for D, we obtain:
D 40 km
Problem 2: Method 2
Another way to solve the problem is by considering the distances in proportion. If in 10 minutes (1/6 hours) she covers 40 km, then:
(1/6 hours) * 48 km/hr 8 km
Thus, 40% of the total distance X is 8 km. Therefore, the total distance is:
0.4X 8 kmX 20 km
This does not match with the initial problem and indicates a need to re-evaluate the given information.
Problem 3: Alternative Approach
Let the total distance x km. The first 60 km takes 0.6x/48 hours, and the remaining 40% (0.4x) of the total distance takes 0.4x/48 hours. According to the given information:
0.6x/48 0.4x/48 1/6
Simplifying, we get:
0.2x/48 1/60.2x 8x 40 km
Problem 4: Detailed Calculation
The first 60 km takes 1 hour to cover. If 10 minutes (1/6 hour) more is needed to cover the remaining part, then:
1 1/6 7/6 hoursTime to cover 40 km 7/6 - 1 1/6 hours40 km 48 km/hr * (1/6) hour40 km is the total distance to her office.
Key Concepts
Distance Speed × Time Time Distance / Speed Speed Distance / TimeConclusion
The total distance to Asha's office is 40 km. This problem illustrates how to use time and speed to determine distance. Understanding these relationships is crucial for solving similar problems efficiently. If you have any more questions or need further assistance, feel free to contact us.