<span>Let m = speed of motorboat
and c = speed of current
.
When going downstream, current speed is added to boat speed -- and, the total speed is "8 miles downstream in 20 minutes"
.
To convert to "miles per hour" we multiply by 60 mins per 1 hour:
(8 miles/20 mins) * (60 mins/1 hour) = 24 mph
.
This gives us our first equation (1):
m+c = 24
.
When going upstream, the boat speed is reduced by the current -- and, the total speed is "8 miles in 30 minutes".
To convert to "miles per hour" we multiply by 60 mins per 1 hour:
(8 miles/30 mins) * (60 mins/1 hour) = 16 mph
.
This gives us our second equation (2):
m-c = 16
m = 16+c
.
Plug the above into equation 1 and solve for c:
m+c = 24
16+c+c = 24
16+2c = 24
2c = 8
c = 4 mph </span>
Answer: y
=
−
2
3
x
+
2
Explanation:
Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
Point-Slope Formula:
y
−
y
1
=
m
(
x
−
x
1
)
, where
m
is the slope of the line and
x
1
and
y
1
are x and y coordinates of a given point.
We can summarize the information already given:
m
=
−
2
3
x
1
=
6
y
1
=
−
2
Using this information, we can substitute these values onto the point-slope formula:
y
−
(
−
2
)
=
−
2
3
(
x
−
(
6
)
)
y
+
2
=
−
2
3
(
x
−
6
)
The equation above is the equation of the line in point-slope form. If we wanted to have the equation in
y
=
m
x
+
b
form then we simply solve the equation above for
y
y
+
2
=
−
2
3
x
+
12
3
y
+
2
−
2
=
−
2
3
x
+
12
3
−
2
y
=
−
2
3
x
+
12
3
−
2
(
3
3
)
y
=
−
2
3
x
+
12
3
−
6
3
y
=
−
2
3
x
+
6
3
y
=
−
2
3
x
+
2y
=
−
2
3
x
+
2
Explanation:
Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
Point-Slope Formula:
y
−
y
1
=
m
(
x
−
x
1
)
, where
m
is the slope of the line and
x
1
and
y
1
are x and y coordinates of a given point.
We can summarize the information already given:
m
=
−
2
3
x
1
=
6
y
1
=
−
2
Using this information, we can substitute these values onto the point-slope formula:
y
−
(
−
2
)
=
−
2
3
(
x
−
(
6
)
)
y
+
2
=
−
2
3
(
x
−
6
)
The equation above is the equation of the line in point-slope form. If we wanted to have the equation in
y
=
m
x
+
b
form then we simply solve the equation above for
y
y
+
2
=
−
2
3
x
+
12
3
y
+
2
−
2
=
−
2
3
x
+
12
3
−
2
y
=
−
2
3
x
+
12
3
−
2
(
3
3
)
y
=
−
2
3
x
+
12
3
−
6
3
y
=
−
2
3
x
+
6
3
y
=
−
2
3
x
+
2
Step-by-step explanation:
Rosa's because about 33% of her floor is covered in toys, while Serena's floor is only covered with 25% toys.
Answer:
10:1
Step-by-step explanation:
Answer:
Step-by-step explanation: