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The steamer going upstream would cover the distance between Town A and Town B in 4 hours and 30 minutes. The same steamer going downstream would cover the distance between the towns in 3 hours. How long would it take a raft moving at the speed of the current to float from B to A?

10 hours
12 hours
15 hours
18 hours
20 hours


18

S = Speed of Steamer
C = Speed of Current

(1) (S-C)*4.5 = d
(2) (S+C)*3 = d
Combining (1) and (2)
4.5S - 4.5C = 3S + 3C
C = S/5
We are looking for (1/C)*d
d = (S + S/5)*3 = 18S/5

(1/C)*d = 5/S * 18S/5 = 18 hour
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Late, but D:

S - distance
t - time
v1 - speed upstream
v2 - speed downstream

Suppose that the distance = 9

4.5 = 9/v1
v1 = 2

3 = 9/v2
v2 = 3

v of the current = 0.5

So the time needed for a raft to travel downstream = 9/0.5 = 18
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let the distance between A and B = X

upstream speed = X/4.5
downstream speed = X/3

speed of the current = (downstream speed - upstream speed)/2
= (X/3 - X/4.5)/2
= X/18

time for the raft = total distance/speed of current = X/(X/18) = 18 hours!!

love luck ;-)
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bmwhype2
The steamer going upstream would cover the distance between Town A and Town B in 4 hours and 30 minutes. The same steamer going downstream would cover the distance between the towns in 3 hours. How long would it take a raft moving at the speed of the current to float from B to A?

A. 10 hours
B. 12 hours
C. 15 hours
D. 18 hours
E. 20 hours

1. For a problem which requires that sum of the speed and difference of the speed respectively be taken considering the direction of an object and in which only the time taken in both the directions are given, we can find the time taken by the slower one of the two, in this case the time taken by an object traveling at the speed of the water current by,

2/ (1/t1 - 1/t2), where t1 is the time taken when sum of the speed is considered and t2 is the time taken when the difference of the speed is considered

2. So we have time time taken by the raft to travel from B to A as 2/ (1/3 - 1/4.5) = 18 hours.
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let the distance between A and B = X

upstream speed = X/4.5
downstream speed = X/3

speed of the current = (downstream speed - upstream speed)/2 .......logic behind divide by 2 or just a formula...
= (X/3 - X/4.5)/2
?????
= X/18

time for the raft = total distance/speed of current = X/(X/18) = 18 hours!!

love luck ;-)

Could not get the above statement.....
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R=Rate of boat
S=Rate of stream

4.5(R-S) = D
3(R+S) = D
4.5(R-S) = 3(R+S)
4.5R- 4.5S = 3R + 3S
1.5R = 7.5S
R = 5S

Plug 5S in the original formula

3(5S+S) = D
15S + 3S = D
18S = D

the Answer is D, 18 hours.
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bmwhype2
The steamer going upstream would cover the distance between Town A and Town B in 4 hours and 30 minutes. The same steamer going downstream would cover the distance between the towns in 3 hours. How long would it take a raft moving at the speed of the current to float from B to A?

A. 10 hours
B. 12 hours
C. 15 hours
D. 18 hours
E. 20 hours

c=speed of current
s=speed of steamer
1=distance one way
s+c=1/3
s-c=1/4.5
subtracting,
2c=1/9
c=1/18 (speed=distance/time)
18 hours
D
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Thank you for the answer I just have small doubt here. when it says in the question that a raft moving at the speed of the current to float from B to A...since it says float from b to a..the answer should be= distance/speed of the current? or, it should be= distance/ 2*speed of the current since it has already has speed of the current and going downstream which is mentioned in the question as it says 'going B to A, therefore the resultant is v+v=2v?
lucky12312
let the distance between A and B = X

upstream speed = X/4.5
downstream speed = X/3

speed of the current = (downstream speed - upstream speed)/2
= (X/3 - X/4.5)/2
= X/18

time for the raft = total distance/speed of current = X/(X/18) = 18 hours!!

love luck ;-)
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DishaSaha
Thank you for the answer I just have small doubt here. when it says in the question that a raft moving at the speed of the current to float from B to A...since it says float from b to a..the answer should be= distance/speed of the current? or, it should be= distance/ 2*speed of the current since it has already has speed of the current and going downstream which is mentioned in the question as it says 'going B to A, therefore the resultant is v+v=2v?
lucky12312
let the distance between A and B = X

upstream speed = X/4.5
downstream speed = X/3

speed of the current = (downstream speed - upstream speed)/2
= (X/3 - X/4.5)/2
= X/18

time for the raft = total distance/speed of current = X/(X/18) = 18 hours!!

love luck ;-)
It will be \(\frac{distance }{ speed of current}\), first case is it goes upstream (speed of boat - speed of current), second downstream (speed of boat + speed of current), and third the boat just floats downstream (speed of current), all three cases are independent.
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