M10-04

Question

A steamer takes 4 hours and 30 minutes to travel from Town A to Town B when traveling upstream against the current. However, it only takes the steamer 3 hours to travel from Town B to Town A when traveling downstream with the current. Assuming the current flows at a constant speed, how long will it take a raft, floating downstream at the speed of the current, to travel from Town B to Town A ?

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

Show Answer

Official Answer

D

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

Bunuel · Accepted Answer

Official Solution:

A steamer takes 4 hours and 30 minutes to travel from Town A to Town B when traveling upstream against the current. However, it only takes the steamer 3 hours to travel from Town B to Town A when traveling downstream with the current. Assuming the current flows at a constant speed, how long will it take a raft, floating downstream at the speed of the current, to travel from Town B to Town A ?

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

Show Answer

Official Answer

D

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

Assume the speed of the steamer in still water is  s  and the speed of the current to is  c .
 
When traveling upstream  against  the current, the steamer's speed is  s - c , and in 4.5 hours it covers a distance of  4.5(s - c) .
 
When traveling downstream  with  the current, the steamer's speed is  s + c , and in 3 hours it covers a distance of  3(s + c) .
 
Since both distances represent the distance between Towns A and B, we can equate them:  4.5(s - c)=3(s + c) , which gives  s = 5c . To express the distance in terms of only one unknown, substitute  s = 5c  in either of the above equations, to get  3(s + c)=18c .
 
To determine how long a raft, floating downstream at the speed of the current, will take to travel from Town B to Town A, we divide the distance between the towns by the speed of the raft:  \frac{distance}{rate}=\frac{18c}{c}=18  hours.

Answer: D

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Sukritvarsh · Answer

So is the effective speed of raft now 2c? ( speed of current + speed of raft which also equals speed of current)?

Bunuel · Answer

No, the effective speed of the raft is not 2c. The raft floats at the same speed as the current, which is just c. Since it has no additional speed of its own, it simply moves at the current's speed, c.

miag · Answer

Hi  Bunuel ,

I am not 100% clear on why the speed of the raft is c and not 2c, isnt it that the effective raft speed will become 2c downstream? Could you explain please?

Thank you so much!

Bunuel · Answer

The key point is that the raft does not have its own propulsion; it moves solely due to the flow of the current. Therefore, its speed is equal to the speed of the current, c.

If the raft had its own propulsion, you could potentially consider adding speeds, but since it simply floats with the current, it cannot go faster than the current itself. Thus, the effective speed of the raft downstream is c, not "c + c" or "2c."

This concept distinguishes between objects with their own propulsion (like the steamer) and those that rely entirely on the current (like the raft).

Shivam2024 · Answer

I don’t quite agree with the solution. It is assumed that speed of raft itself is 0. Poor question framing.

Bunuel · Answer

A raft is a simple, flat, floating structure made of materials like logs or planks, often without any engine, motor, or sails. It doesn't generate its own movement. So when placed in a river, it just drifts with the flow of the water, that is, it moves at the speed of the current.

So, in general a raft has no independent speed. Its motion depends entirely on external forces, like a river current. That’s why, in this question, the raft's speed is taken as equal to the current’s speed.

vp20 · Answer

I like the solution - it’s helpful.

Vijay_K · Answer

I like the solution - it’s helpful.

Shubham2599jain · Answer

Bunuel 
If the boat is floating downstream at the speed of the current, doesn't it mean 2*speed of the current, implying speed of boat (which is equal to that of current) x the speed of current

Bunuel · Answer

Floating means the raft is just carried by the river. So its speed relative to the water is 0, and its speed relative to the shore is c, not 2c.

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