Ankur takes 2 hrs more than Sanjay to cover a certain distance. If Ankur doubles his speed, then he takes 6 hrs less than Sanjay to cover twice the same distance. Find the time taken by Sanjay to cover the distance.
Question
Ankur takes 2 hrs more than Sanjay to cover a certain distance. If Ankur doubles his speed, then he takes 6 hrs less than Sanjay to cover twice the same distance. Find the time taken by Sanjay to cover the distance.
Solution
Let's denote the time taken by Sanjay to cover the distance as 'S' (in hours). According to the problem, Ankur takes 2 hours more than Sanjay to cover the same distance, so we can denote the time taken by Ankur as 'S + 2'.
The problem also states that if Ankur doubles his speed, he takes 6 hours less than Sanjay to cover twice the distance. Doubling the speed means halving the time, so the time taken by Ankur to cover twice the distance at double speed is '(S + 2) / 2'. According to the problem, this is 6 hours less than the time taken by Sanjay to cover the same distance, which is '2S'. So we can write the equation:
(S + 2) / 2 = 2S - 6
Solving this equation will give us the time taken by Sanjay to cover the distance.
First, multiply all terms by 2 to get rid of the fraction:
S + 2 = 4S - 12
Then, rearrange the equation to isolate 'S':
3S = 14
Finally, divide by 3 to solve for 'S':
S = 14 / 3 ≈ 4.67 hours
So, Sanjay takes approximately 4.67 hours to cover the distance.
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