Question 381454: i need your help to this problem. can you help me?here's the prob.
A man is at a point A on the bank of a straight river. he can row in a still water at a rate which is 20 per cent faster than he can walk. if he rows downstream to a point B, which is 4 mi. below A and on the same side of the river, and then walks, in a direction which is perpendicular to the river, to a point C, 3mi. from B, it takes him the same amount of time that it thus to walk straight from A to c. if he walks back from C to B and then rows upstream to A, the return trip takes him an hour and 36min. longer. find his rate of walking, his rate of rowing in still water, and the rate of the current of the river.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! ...
This is a multi stage problem
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Let walking rate be x mph
Rowing rate in still water = 1.2x ( 20% more)
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Let rate of current = y mph
Calculate time A---->B-------->C
Ato B (down stream)
time = 4/(1.2x+y)
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B to C (walk)
time = 3/x
Time A to B to C
=4/(1.2x+y)+3/x
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AC ^2 = AB^2 +BC^2
AC^2=4^2+3^2
AC^2=25
AC = 5 miles
Time to walk from A to C = 5/x
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Time from A to B to C = Time from A to C (walking)
4/(1.2x+y) + 3/x = 5/x
4/(1.2x+y)= 5/x-3/x
4/(1.2x+y)= 2/x
cross multiply
4x=2(1.2x+y)
4x=2.4x+2y
4x-2.4x=2y
1.6x=2y
/2
0.8x= y speed of current
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TIME RETURN
3/x + 4/(1.2x-y)(upstream)
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Time return - time forward = 8/5 hours
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(3/x + 4/(1.2x-y))- (4/(1.2x+y) + 3/x)= 8/5
y=0.8x
plug value of y
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(3/x + 4/(1.2x-0.8x))- (4/(1.2x+0.8x) + 3/x)= 8/5
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(3/x +4/0.4x)-(4/2x+3/x)=8/5
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(3/x+10/x)-(2/x+3/x)=8/5
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(13/x)-(5/x)=8/5
8/x=8/5
x=5 mph rate of walk.
Rate of rowing in still water = 1.2x = 1.2 * 5 = 6 mph.
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Cheers
m.ananth@hotmail.ca
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