A crew can row a certain course up the stream in 84
minutes; they can row the same course down stream
in 9 minutes less than they can row it in still water. How long would they take to row down with the stream.
Answers
Answer:
ANSWER
Let the speed of the boat in still water be x
And speed of the stream be y
Also, let the length of the course is d
The speed of the boat upstream is x−y
Time taken for the boat to row upstream is
x−y
d
=84 (1)
Time taken in still water is
x
d
The speed of the boat in downstream is x+y
Time taken in downstream is
x+y
d
According to the question,
x
d
−
x+y
d
=9
⇒
x×(x+y)
dy
=9 (2)
Dividing (2) from (1) we get,
(
x
y
)×
x+y
x−y
=
28
3
⇒(
x
y
)×(
1+(
x
y
)
1−(
x
y
)
)=
28
3
Let (
x
y
)=k
⇒k×
1+k
1−k
=
28
3
⇒28k
2
−25k+3=0
⇒k=
7
1
or k=
4
3
From equation (1),
x−y
d
=84
⇒
x
d
×
1−(
x
y
)
1
=84
⇒
x
d
×
1−k
1
=84
Putting k=
7
1
,
x
d
=84×
7
6
=72 minutes
So, time taken to row in downstream =
x+y
d
=
x
d
×
1+k
1
=72×
8
7
=63 minutes
Putting k=
4
3
,
x
d
=84×
4
1
=21 minutes
So, time taken to row in downstream =
x+y
d
=
x
d
×
1+k
1
=21×
7
4
=12 minutes