In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 3$ votes cast for candidate A, candidate B got $\displaystyle 1$ vote. We can write the following ratio.

$\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$\displaystyle 3:1\rightarrow \frac{3}{1}$

We know that candidate B received $\displaystyle 900$ votes. Write a new ratio.

$\displaystyle A:900\rightarrow\frac{A}{900}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\displaystyle \frac{3}{1}=\frac{A}{900}$

Cross multiply and solve for $\displaystyle A$.

$\displaystyle 1(A)=900(3)$

Simplify and solve.

$\displaystyle A=2700$

In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 7$ votes cast for candidate A, candidate B got $\displaystyle 1$ vote. We can write the following ratio.

$\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$\displaystyle 7:1\rightarrow \frac{7}{1}$

We know that candidate B received $\displaystyle 134$ votes. Write a new ratio.

$\displaystyle A:134\rightarrow\frac{A}{134}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\displaystyle \frac{7}{1}=\frac{A}{134}$

Cross multiply and solve for $\displaystyle A$.

$\displaystyle 1(A)=134(7)$

Simplify and solve.

$\displaystyle A=938$

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$\displaystyle 195\ miles: 5\ hours=\frac{195\ miles}{5\ hours}$

Reduce and solve.

$\displaystyle 39mph$

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$\displaystyle 2035\ miles: 37\ hours=\frac{2035\ miles}{37\ hours}$

Reduce and solve.

$\displaystyle 55mph$

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$\displaystyle 180\ miles: 3\ hours=\frac{180\ miles}{3\ hours}$

Reduce and solve.

$\displaystyle 60mph$

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$\displaystyle 360\ miles: 8\ hours=\frac{360\ miles}{8\ hours}$

Reduce and solve.

$\displaystyle 45mph$

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$\displaystyle 2310\ miles: 55\ hours=\frac{2310\ miles}{55\ hours}$

Reduce and solve.

$\displaystyle 42\textup{ mph}$

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$\displaystyle 1445\ miles: 17\ hours=\frac{1445\ miles}{17\ hours}$

Reduce and solve.

$\displaystyle 85mph$

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$\displaystyle 60\ miles: 1\ hour=\frac{60\ miles}{1\ hour}$

Reduce and solve.

$\displaystyle 60mph$

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$\displaystyle 723\ miles: 3\ hours=\frac{723\ miles}{3\ hours}$

Reduce and solve.

$\displaystyle 241mph$