In covering distance, the speeds of A & B are in the ratio of 3:4.A takes 30min more than B to reach the destination. Find time taken by A to reach the destination?
if a and b are the times, since the speeds are in ratio 3/4, the times are related by
a/b = 4/3
a = b+30
a = 120
b = 90
To find the time taken by A to reach the destination, let's first assign some variables.
Let the speed of A be 3x (in any consistent unit, such as km/h) and the speed of B be 4x.
Now, we are given that A takes 30 minutes (or 0.5 hours) more than B to reach the destination. This means that the time taken by A is the time taken by B plus 0.5 hours.
Let's denote the time taken by B as t. Therefore, the time taken by A can be represented as t + 0.5.
Now, we can use the formula:
Distance = Speed × Time
Since the distance covered by A and B is the same (as they are both reaching the same destination), we can equate their respective expressions for distance.
Distance covered by A = Distance covered by B
(Speed of A) × (Time taken by A) = (Speed of B) × (Time taken by B)
(3x) × (t + 0.5) = (4x) × t
Next, we can solve this equation to find the value of t, which represents the time taken by B.
3xt + 1.5x = 4xt
1.5x = xt
1.5 = t
Therefore, we have found that t is equal to 1.5 hours, which represents the time taken by B.
To find the time taken by A, we substitute this value for t into the expression t + 0.5:
Time taken by A = t + 0.5
Time taken by A = 1.5 + 0.5
Time taken by A = 2 hours
So, A takes 2 hours to reach the destination.