At his usual rowing rate Rahul can travel 12 miles downstream in a certain river in 6 hours less tha...........

Quantitative Aptitude ( CCS) Boats and Streams

At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour?

2 2/3 mph

2 mph

1 1/4 mph

3 mph

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Explanation:

Solution:
Let the speed of Rahul in still water be x mph
and the speed of the current be y mph
Then, Speed upstream = (x – y) mph
Speed downstream = (x + y) mph
Distance = 12 miles
Time taken to travel upstream – Time taken to travel downstream = 6 hours
12/(x-y) – 12/(x+y)=6
x²=y²+4y—1
Now he doubles his speed. i.e., his new speed = 2x
Now, Speed upstream = (2x – y) mph
Speed downstream = (2x + y) mph
In this case, Time taken to travel upstream – Time taken to travel downstream = 1 hour
12/(2x-y) – 12/(2x+y) = 1
4x²=y²+24y—2
From 1 and 2 we get
4y+y²=(24y +y²)/4
Y=8/3==> 2 2/3mph