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.