Boats and streams problem...

[Wise geek]

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 will take only one hour less than the upstream 12 miles. What is the speed of the current in miles per hour??

Answer-8/3 mph

[loveFluffy]

let's presume the speed of the current in miles per hour is "x" and his usual rowing rate is v(so that's apparently the double rowing rate is: 2v)

at his usual rowing rate, it takes him "t" hours to upstream and "t-6" hours to downstream

at his double rowing rate, it takes him t' hours to upstream and t'-1 hours to downstream

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and then we get those equations:

eq1: (v+x)(t-6)=12

eq2: (v-x)t=12

eq3: (2v+x)(t'-1)=12

eq4: (2v-x)t'=12

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There are four equations and four unknown variables, so there must be at least one answer for this question, let's see how to get the exact value of "x":

first, we can get this by combining eq1 and eq2:

eq5: v*v=x*x+4*x

and similarly, we can get this by combining eq3 and eq4:

eq6: 4*v*v=x*x+24*x

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then replace the "v*v" of eq6 with x*x+4*x, we can get this:

eq7: 3*x*x=8*x

which means x=0 or x=8/3

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obviously, x can not be 0 (because the time of upstream and downstream must be different)

so, the answer is 8/3

 

Good luck~