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ellenweiklee8581
17.12.2019 •
Mathematics
Amotorboat travels 244 kilometers in 4 hours going upstream and 749 kilometers in 7 hours going downstream. what is the rate of the boat in still water and what is the rate of the current
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Ответ:
Speed of Motorboat = 84 kmph
Speed of Current = 23 kmph
Step-by-step explanation:
Distance Equation is:
D = RT
Where
D is distance
R is rate
T is time
Downstream rate is rate of boat PLUS current
Upstream rate is rate of boat MINUS current
Let rate of boat be "x" and rate of current be "c".
From first statement, we can write:
244 = (x - c)(4)
From second statement, we can write:
749 = (x + c)(7)
The first equation becomes:
244 = 4x - 4c
The second equation becomes:
749 = 7x + 7c
Multiplying first equation by 7 , we have:
7 * [244 = 4x - 4c] = 1708 = 28x - 28c
Multiplying 2nd equation by 4, we have:
4 * [749 = 7x + 7c] = 2996 = 28x + 28c
Now we add up these equations (in bold):
1708 = 28x - 28c
2996 = 28x + 28c
4704 = 56x
x = 4704/56
x = 84
Now using this value and plugging in original equation, we can find "c":
244 = 4x - 4c
244 = 4(84) - 4c
244 = 336 - 4c
4c = 92
c = 92/4
c = 23
Speed of Motorboat = 84 kmph
Speed of Current = 23 kmph
Ответ:
Step-by-step explanation: