Question

A casino riverboat travels up the Mississippi Rive at 12 mph and then back to its original port at a rate of 15 mph. The round trip take 7.5 hours. What is the total distance traveled by the riverboat?

Answer 1

Speed up to Mississippi Rive = 12 mph

Speed back to original port = 15 mph

Total time taken by the riverboat = 7.5 hours

Total distance covered = ?

We know that the distance covered each side would be the same.

So Distance up to Mississippi Rive = Distance back to original port

⇒ ${\text} Speed up to Mississippi Rive * Time taken to reach Mississippi Rive = Speed back to the original port * Time back to the original port$ .......... (i)

Let Time taken to reach Mississippi Rive = x .............. (ii)

⇒ Time taken to reach back to original port = 7.5 - x .......... (iii)

Substituting (ii) and (iii) in (i)

⇒ ${\text} 12 * x = 15 * (7.5 - x)$

⇒ ${\text} 12x = 112.5 - 15x$

⇒ ${\text} 27x = 112.5$

⇒ ${\text} x = [tex]\frac{112.5}{27}$ [/tex]

Using value of x to determine distance traveled:

Distance Traveled up to Mississippi Rive = ${\text}Speed up to Mississippi Rive * Time taken to reach Mississippi Rive$

⇒ Distance Traveled up to Mississippi Rive = ${\text}12 * \frac{112.5}{27}$

⇒ Distance Traveled up to Mississippi Rive = 50 miles

Hence, the riverboat traveled total of 50 + 50 = 100 miles

Answer 2

Since this is a round trip the journey covered the same distance.

Let $t_1$ represent the time and  

$d$ represent the distance in the first.

We were told that the boat traveled at 12 mph

$12=\frac{d}{t_1}$

$\frac{d}{12}=t_1$

Let $t_2$ represent the time and  

$d$ represent the distance in the return trip.

During this returned trip the boat travelled at 15mph

$t_2=\frac{d}{15}$

Adding the total time should give us 7.5 hours

$\frac{d}{15}+\frac{d}{12}=7.5$

$\frac{3}{20}d=7.5$

$d=\frac{7.5}{\frac{3}{20}}$

$d=50$

The total distance traveled is

$d+d=50+50=100$ miles