Question

The distance from City A to City B is about 93 mi by ferry. It takes 2 hr less to travel by the same ferry from City B to City​ C, a distance of about 62 mi. What is the average rate of the​ ferry?

Answer 1

Let's denote the average rate of the ferry as \( r \) (in miles per hour).

From City A to City B, the distance is 93 miles. The time taken to travel this distance can be expressed as:

\[
\text{Time from A to B} = \frac{93}{r}
\]

From City B to City C, the distance is 62 miles. The time taken to travel this distance can be expressed as:

\[
\text{Time from B to C} = \frac{62}{r}
\]

According to the problem, the time from City B to City C takes 2 hours less than the time from City A to City B. Therefore, we can write the equation:

\[
\frac{62}{r} = \frac{93}{r} - 2
\]

Now, we can eliminate the fractions by multiplying through by \( r \):

\[
62 = 93 - 2r
\]

Next, we can solve for \( r \):

\[
2r = 93 - 62
\]
\[
2r = 31
\]
\[
r = \frac{31}{2}
\]
\[
r = 15.5
\]

Thus, the average rate of the ferry is \( 15.5 \) miles per hour.