Chapter 1, Problem 7PS

a.

To determine

To calculate: the total duration of the voyage in hours

Answer to Problem 7PS

Total time $=\frac{245}{3}$ hours

Explanation of Solution

Given:

At 2:000 P.M. on April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 P.M. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approx. 3400-mile trip.

Calculation:

From 2:000 P.M. in April 11, to 11:40 P.M. on April 14, total time is 3 days, 9 hours, and 40 minutes.

1 day = 24 hours and 1 minute $=\frac{1}{60}$ hours,

So total time will be

  $\begin{array}{c}3\times 24+9+40\times \frac{1}{60}=72+9+\frac{2}{3}\\ =\frac{245}{3}\text{hours}\end{array}$

b.

To determine

To calculate: the average speed in miles per hour

Answer to Problem 7PS

Average speed $\text{=}\frac{180}{7}\text{mph}$

Explanation of Solution

Given:

At 2:000 P.M. in April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 P.M. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approx. 3400-mile trip.

Concept used:

Average speed $\text{=}\frac{\text{Distance}\text{Travelled}}{\text{Total}\text{time}}$

Calculation:

Average speed $\text{=}\frac{\text{2100}}{\frac{245}{3}}\text{=2100}\times \frac{3}{245}\text{=}\frac{180}{7}\text{mph}$

c.

To determine

To calculate: the domain and range of the function and write a function relating the distance from New York City and the number of hours traveled.

Answer to Problem 7PS

Domain of the function is $0\le x\le \frac{245}{3}$

Range of function is $1300\le y\le 3400$

The function related to distance is $y=-\frac{180}{7}x+3400$

Explanation of Solution

Given:

At 2:000 P.M. in April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 P.M. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approx. 3400-mile trip.

From above parts we the total duration of journey is $\frac{245}{3}$ hours.

Calculation:

First we find the domain.

Let x represent the total time in hours.

Since total duration of journey is $\frac{245}{3}$ hours., domain of the function is $0\le x\le \frac{245}{3}$

Now we find the range,

Given: Distance of journey = 3400 mile

Distance of ship from Ireland = 2100 miles

Let distance of ship from New York = y

Then, Distance of ship from New York = Distance of journey - Distance of ship from Ireland

=3400-2100

=1300 miles

At the time of collision, $y=1300$ miles

As the minimum value of y is 1300 and maximum value of y is 3400. So,

Range of function is $1300\le y\le 3400$ .

Now we find the equation of the line passing through $\left(0,3400\right)\&\left(\frac{245}{3},1300\right)$

Using two point form of straight line,

  $\begin{array}{l}y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\\ y=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)+y_1\\ y=\frac{1300-3400}{\frac{245}{3}-0}\left(x-0\right)+3400\\ y=-\frac{180}{7}x+3400\end{array}$

d.

To determine

To plot: the function in part (c).

Answer to Problem 7PS

  

Explanation of Solution

Given:

At 2:000 P.M. in April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 P.M. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approx. 3400-mile trip.

The function from the above part is $y=-\frac{180}{7}x+3400$

Calculation:

For graph plot the starting point $\left(0,3400\right)$ and the end point $\left(\frac{245}{3},1300\right)$ from the above part and then draw a line segment joining above points.