Acasino 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?

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

⇒ .......... (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)

⇒

⇒

⇒

⇒ " alt="\frac{112.5}{27}" /> " />

Using value of x to determine distance traveled:

Distance Traveled up to Mississippi Rive =

⇒ Distance Traveled up to Mississippi Rive =

⇒ Distance Traveled up to Mississippi Rive = 50 miles

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

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

Let represent the time and  

represent the distance in the first.

We were told that the boat traveled at 12 mph

Let represent the time and  

represent the distance in the return trip.

During this returned trip the boat travelled at 15mph

Adding the total time should give us 7.5 hours

The total distance traveled is

miles