Answer:
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
<u>Speed of Motorboat = 84 kmph</u>
<u>Speed of Current = 23 kmph</u>
