On a market day Mrs.lana walks to the market from her home at steady speed. This journey normally takes her 2 hours to complete.
She finds, however that by increasing her speed in km/hr.she can save 20 minutes. Find her usual speed in km/hr?
d = r1*t,
d = r1 * 2
r1 = d/2 = Her usual speed
d = r2 * (2-1/3) = r * (6/3-1/3) = r2 * 5/3,
r2 = 3d/5.
r2/r1 = (3d/5)/(d/2) = 3d/5 * 2/d = 6/5.
r1 = 5r2/6.
I need to know her 2nd rate(r2).
To solve this problem, we need to set up a mathematical equation using the given information.
Let's first convert the time taken in hours to minutes. We are given that Mrs. Lana's journey normally takes her 2 hours, which is equivalent to 2 x 60 = 120 minutes.
Let's assume her usual speed is x km/hr. Therefore, the distance she covers can be calculated using the formula: Distance = Speed x Time.
Using the above formula, we can write the equation for her usual speed as follows: x km/hr * 2 hours = Distance.
Now, let's consider the second scenario where she increases her speed in km/hr to save 20 minutes. We need to convert 20 minutes to hours, which is 20/60 = 1/3 hours.
In this case, the distance she covers is the same, but she takes 2 hours – 1/3 hours = 5/3 hours to complete the journey.
Using the formula Distance = Speed x Time and substituting the values, we can write the equation for her increased speed as follows: (x + y) km/hr * (5/3) hours = Distance.
Since the distance remains the same in both cases, we can equate the two equations:
x km/hr * 2 hours = (x + y) km/hr * (5/3) hours.
Simplifying the equation, we get:
2x = (5/3)(x + y).
To solve for Mrs. Lana's usual speed (x), we can rearrange the equation:
6x = 5x + 5y.
Subtracting 5x from both sides of the equation, we get:
x = 5y.
So, Mrs. Lana's usual speed is five times her increased speed.
In this case, her increased speed is calculated by converting the saved time from minutes to hours: 20/60 = 1/3 hours.
Therefore, her usual speed (x) is five times her increased speed (1/3 * y):
x = 5 * (1/3)
x = 5/3 km/hr.
Hence, Mrs. Lana's usual speed is 5/3 km/hr.