The time taken to travel between two towns varies inversely with the average speed is 42km/hours,the journey takes 4hour.find the average speed if the journey takes 2hours 20 minutes
t = k/s
so ts is constant
you want s such that
8/3 s = 4*42
now finish it off
Answer
To find the average speed if the journey takes 2 hours and 20 minutes, we need to determine the constant of variation, which relates the time taken to travel between two towns and average speed.
Let's denote the time taken as T and the average speed as S.
According to the problem statement, the time taken to travel between two towns varies inversely with the average speed. This can be expressed as:
T ∝ 1/S
where ∝ denotes "varies inversely."
We are given that the average speed is 42 km/hour when the journey takes 4 hours. Using this information, we can form the equation:
4 ∝ 1/42
To solve for the constant of variation (∝), we can cross multiply:
4 * 42 = 1 * T
168 = T
Therefore, we found that when the journey takes 4 hours, the time taken is 168 minutes.
Now, to find the average speed when the journey takes 2 hours and 20 minutes, we need to convert the time into minutes. Since there are 60 minutes in one hour, 2 hours and 20 minutes can be expressed as:
2 hours + 20 minutes = 2 * 60 + 20 = 140 minutes
Let's denote this time as T2, and the average speed as S2. We can set up the equation based on the constant of variation found earlier:
T2 ∝ 1/S2
Plugging in the values we have:
140 ∝ 1/S2
Using the same constant of variation (∝) found earlier, we have:
168 = 1/S2
To find S2, we can solve for it:
S2 = 1/168
Using a calculator, we find:
S2 ≈ 0.00595238
Thus, the average speed for the journey that takes 2 hours and 20 minutes is approximately 0.00595238 km/minute.