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The Lirr River runs from Rosedale in the west to Oceanside i
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31 Jan 2020, 05:39
31 Jan 2020, 05:39
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Question Stats:
54% (02:38) correct
45% (00:40) wrong based on 11 sessions
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The Lirr River runs from Rosedale in the west to Oceanside in the east with the current moving at an average of 10 miles per hour. Sasha is traveling by motorboat from Oceanside to Rosedale and back. If the water were not moving, Sasha’s motorboat would travel at an average speed of 20 miles per hour. Given the current, what was Sasha’s actual average speed, in miles per hour, for the round trip?
Show: :: Miles
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Re: The Lirr River runs from Rosedale in the west to Oceanside i
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31 Jan 2020, 11:26
31 Jan 2020, 11:26
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Carcass wrote:
The Lirr River runs from Rosedale in the west to Oceanside in the east with the current moving at an average of 10 miles per hour. Sasha is traveling by motorboat from Oceanside to Rosedale and back. If the water were not moving, Sasha’s motorboat would travel at an average speed of 20 miles per hour. Given the current, what was Sasha’s actual average speed, in miles per hour, for the round trip?
Show: :: Miles
15
Considering the current:
Speed downstream (D) = speed of boat + Speed of current = 20 + 10 = 30 miles/hr
Speed upstream (U) = speed of boat - Speed of current = 20 - 10 = 10 miles/hr
Since in the round-trip, distance traveled downstream = distance traveled upstream, we have:
Average speed = \(\frac{2*D*U}{(D + U)} = \frac{2*30*10}{(30 + 10)}\) = 15 miles/hr
Alternate approach:
Let distance = D miles
Time taken to travel downstream = D/30 hr
Time taken to travel upstream = D/10 hr
Total time = (D/30 + D/10) = 4D/30 hr
Total distance = D + D = 2D miles
=> Average speed = \(\frac{2D}{(4D/30)}\) = 15 miles/hr
[We could also have chosen some suitable value of D (say 300 miles) and performed the above calculation]
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The Lirr River runs from Rosedale in the west to Oceanside i
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18 Feb 2021, 07:02
18 Feb 2021, 07:02
Carcass wrote:
The Lirr River runs from Rosedale in the west to Oceanside in the east with the current moving at an average of 10 miles per hour. Sasha is traveling by motorboat from Oceanside to Rosedale and back. If the water were not moving, Sasha’s motorboat would travel at an average speed of 20 miles per hour. Given the current, what was Sasha’s actual average speed, in miles per hour, for the round trip?
Show: :: Miles
15
Let the distance (one-way) be \(x\) miles
\(t_1\) be time taken to go downstream
\(t_2\) be time taken to go upstream
Speed of current = 10 mph
Speed of motorboat = 20 mph
Relative speed going downstream = 20 + 10 = 30 mph
Relative speed going upstream = 20 - 10 = 10 mph
Average speed = \(\frac{total distance}{total time} = \frac{2x}{(t_1 + t_2)}\)
\(t_1 = \frac{x}{30}\)
\(t_2 = \frac{x}{10}\)
So,
Average speed = \(\frac{(2x)(30)}{4x}\)
= 15 mph
