Answer: the rate of the canoeist in calm water is 6 mph and the rate of the current is 4 mph
Step-by-step explanation:
Let x represent the rate of the canoeist in calm water.
Let y represent the rate of the current.
The canoeist travels 30 miles downstream in three hours.. Assuming that he travelled in the direction of the current, his total speed would be x + y mph
Distance = speed × time
Distance covered downstream is
30 = 3(x + y)
10 = x + y - - - - - - - - - - - -1
Against the current the return trip took fifteen hours..
His total speed would be x - y mph
Distance = speed × time
Distance covered on return trip is
30 = 15(x - y)
2 = x - y - - - - - - - - - - - -2
Adding equation 1 and equation 2, it becomes
12 = 2x
x = 12/2 = 6 mph
Substituting x = 6 into equation 1, it becomes
10 = 6 + y
y = 10 - 6 = 4 mph
Answer:
The equation is y=0.30x
Step-by-step explanation:
In order to get the discounted price, one must multiply the 30% (or 0.30 in decimals) by the orignal value of the ticket, which is x.
Basically, we have to find out what 72% of 92 minutes is. A way to do this is turn 92 minutes into a decimal: 92 / 100 = 0.92 and then multiply the decimal by 72: 0.92 x 72 = 66.24 minutes. Rounding to the nearest tenth, however, changes the number to 66.2 minutes. Hope this helps!
Answer:
6:5:2
Step-by-step explanation:
We need the amounts for v to be equal, so
u:v = 12:10 v is 10
v:w = 25:17 v is 25
Multiply the first ratio by 2.5 to get an equivalent amount for v
u:v = 30:25
so u:v:w = 30:25:10
They can all be divided by 5
6:5:2
Answer:
Given the equation: ![3x^2+14x+16=0](https://tex.z-dn.net/?f=3x%5E2%2B14x%2B16%3D0)
The general equation of quadratic formula for
where a, b and c are constant;
then, the solution for this equation is given by;
......[1]
From the equation,
we have
a =2, b=14 and c=16
Substitute these values in [1] to solve for x;
or
![x=\frac{-14\pm\sqrt{196-192}}{6} =\frac{-14\pm\sqrt{4}}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-14%5Cpm%5Csqrt%7B196-192%7D%7D%7B6%7D%20%3D%5Cfrac%7B-14%5Cpm%5Csqrt%7B4%7D%7D%7B6%7D)
Simplify:
![x=\frac{-14\pm\sqrt{4}}{6} =\frac{-14\pm 2}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-14%5Cpm%5Csqrt%7B4%7D%7D%7B6%7D%20%3D%5Cfrac%7B-14%5Cpm%202%7D%7B6%7D)
then,
and
![x=\frac{-14-2}{6} =\frac{-16}{6} =\frac{-8}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-14-2%7D%7B6%7D%20%3D%5Cfrac%7B-16%7D%7B6%7D%20%3D%5Cfrac%7B-8%7D%7B3%7D)
Therefore, the solutions for the given equation is; x =-2 and ![x =-\frac{8}{3}](https://tex.z-dn.net/?f=x%20%3D-%5Cfrac%7B8%7D%7B3%7D)