A man is going near a boatyard daily as a habit. Everyday he hires a boat from there & row it down to the next boatyard.Then he keeps the boat there & start swimming to the place he hired the boat. The river has a constant speed of
4
m
s
−
1
. He do not apply any force in rowing the boat. So then the speed of the traveling boat will be the same as the river. (This man has an uniform speed in swimming).
One day he applied a force to row the boat & increased the speed by 6 m s − 1 .That day he was 4 1 minutes early to the place he hired the boat.
What is the distance between the two boat yards in meters?
Note:- No time is wasted in the boatyards.
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We know that: d i s t a n c e = v e l o c i t y × t i m e
We don't know the time exactly but we know the speed. Imagine that t is time needed to cross the river with boat without any force by the man.
d = 4 . t = 4 t and also d = ( 4 + 6 ) . ( t − 1 / 4 m i n u t e s ) = 1 0 t − 2 . 5 m i n u t e s
d = d
4 t = 1 0 t − 2 . 5 m i n u t e s
6 t = 2 . 5 m i n u t e s
6 t = 2 . 5 x 6 0 s e c o n d
t = 2 5 s e c o n d
input t to the distance will give us d = 4 . 2 5 = 1 0 0 m
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Let,
time spend for the full journey be t,
distance between the 2 boatyards be d,
the uniform swimming speed of the man be s.
t i m e = s p e e d d i s t a n c e ,
t = 4 m s − 1 d + s − 4 m s − 1 d ------------------- 1
t − 1 5 s = 1 0 m s − 1 d + s − 4 m s − 1 d ------------------ 2
1 − 2
1 5 s = 4 m s − 1 d − 1 0 m s − 1 d
1 5 s = 4 0 m s − 1 1 0 d − 4 d
1 5 s = 4 0 m s − 1 6 d
6 d = 6 0 0 m
d = 1 0 0 m
So the answer in meters will be -------------------------------100