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

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=(d)/(t_1)`

`(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=(d)/(15)`

Adding the total time should give us 7.5 hours

`(d)/(15)+(d)/(12)=7.5`

`(3)/(20)d=7.5`

`d=(7.5)/((3)/(20))`

`d=50`

The total distance traveled is

`d+d=50+50=100` miles

Answer 2

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](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 * (112.5)/(27)`

⇒ Distance Traveled up to Mississippi Rive = 50 miles

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