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Bunuel
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MegB07
Hi why re we adding the speeds when going in the same direction?
Because when the boat goes from A to B, the current is pushing it forward in the same direction.

  • Boat’s own still-water speed = x mph
  • Current’s speed = 3 mph
  • Effective speed with the current = x + 3 mph

That’s why we add the speeds.

On the way back, the current resists the motion, so the effective speed is x - 3 mph.
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Hi MegB07


If the relative speed concept is used, then you are right, it should be subtracted. And thus Ship speed will be 33 miles/Hour. But here in that case the return journey will take less time than the initial journey, which is against what the question stem says.

This question is an application of speed, distance than relative velocity.


MegB07
Hi why re we adding the speeds when going in the same direction?
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Hi Bunuel
Could you please explain why using the formula Sr=(2*S1*S2)/(S1+S2) doesn't work for the round trip's average ? I am trying to use this formula as the distance is the same for both runs but can't get the correct answer.
Thank you
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Omnoui
Hi Bunuel
Could you please explain why using the formula Sr=(2*S1*S2)/(S1+S2) doesn't work for the round trip's average ? I am trying to use this formula as the distance is the same for both runs but can't get the correct answer.
Thank you

The formula actually does work here.

For the round trip, the two actual speeds are

  • with current: 30 mph
  • against current: 24 mph

So the average speed is

(2 * S1 * S2)/(S1 + S2) =

= (2 * 30 * 24)/(30 + 24) =

= 1440/54 =

= 26 2/3 mph.
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I like the solution - it’s helpful.
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I like the solution - it’s helpful.
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Bunuel
Average Speed cant be (S1+S2)/2 right ?
Just to double check
I found myself confused if that can be used!!
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Bunuel
Average Speed cant be (S1+S2)/2 right ?
Just to double check
I found myself confused if that can be used!!

Correct, you cannot use (S1 + S2)/2 here.

That works only when the time spent at each speed is the same. Here the ship travels the same distance each way, but the times are different, so average speed must be total distance/total time.
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Solution:

By following the matrix approach we can deal with this problem.

As we know speed of the current is 3 miles per hour and let's assume the speed of the still water is x.

Speed against the current is x-3 and with the current is x+3.



SpeedTime Distance
x+34120
x-3?120

Let's calculate the still speed

Speed = Distance/Time

x+3 = 120/4 = 27 miles per hour.

Time ( against the current) = 120/(27-3)=5 hours

Average speed = Total Distance/Total Time=>240/9 = 26 2/3



Bunuel
A cruise ship travels between two islands, Island A and Island B, which are 120 miles apart. The cruise ship operates at a constant speed in still water. However, a current flows at a constant speed of 3 miles per hour.

On the trip from Island A to Island B, the ship travels with the current and completes the journey in 4 hours. On the return trip, against the current, it takes longer to complete the journey.

Based on the above information, select for Still Speed the cruise ship’s speed in still water, in miles per hour and for Average Speed the ship’s average speed for the round trip, in miles per hour.
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