Ashok covers 60 km in 1.5 hours with the wind and 2 hours against the wind. Find Ashok's speed and the speed of wind.
since distance = speed * time, if Ashok's speed is a, and thw wind's is w, then we have
(3/2)(a+w) = 60
(2)(a-w) = 60
Not good
To solve this problem, we can use the concept of relative speed. Let's assume Ashok's speed in still air is S km/h, and the speed of the wind is W km/h.
When Ashok is traveling with the wind, his effective speed will be increased due to the wind's assistance. So, Ashok's speed with the wind will be (S + W) km/h.
On the other hand, when Ashok is traveling against the wind, the wind will act as a resistance, reducing his effective speed. So, Ashok's speed against the wind will be (S - W) km/h.
Now, let's calculate the distances Ashok covers in the given time durations:
When traveling with the wind, the distance covered is 60 km, and the time taken is 1.5 hours. Therefore, using the formula Distance = Speed * Time:
60 = (S + W) * 1.5
When traveling against the wind, the distance covered is 60 km, and the time taken is 2 hours:
60 = (S - W) * 2
Now, we have a system of two equations with two variables (S and W). Solving these equations simultaneously will give us the values of S (Ashok's speed) and W (the speed of the wind).
Let's proceed to solve these equations:
From the first equation: 60 = (S + W) * 1.5
Dividing both sides of the equation by 1.5:
40 = S + W - Equation 1
From the second equation: 60 = (S - W) * 2
Dividing both sides of the equation by 2:
30 = S - W - Equation 2
Now, we have a system of linear equations. We can solve them using any of the methods, such as substitution or elimination.
Using the elimination method, we can subtract Equation 2 from Equation 1 to eliminate the variable W:
(40) - (30) = (S + W) - (S - W)
10 = 2W
Dividing both sides of the equation by 2:
W = 5
Now, substitute the value of W (5) in either Equation 1 or Equation 2 to calculate S:
40 = S + 5
S = 40 - 5
S = 35
Therefore, Ashok's speed in still air is 35 km/h, and the speed of the wind is 5 km/h.
Hence, Ashok's speed is 35 km/h, and the speed of the wind is 5 km/h.