Aboat takes 8 hours to go 6 miles upstream and come back to the starting point. if the speed of the boat is 4 miles per hour in still water, what is the rate of the current? hint: total time taken = time taken to go upstream + time taken to go downstream `"time taken to go upstream" = "distance"/"speed of boat in still water + rate of current"` ` ` `"time taken to go downstream" = "distance"/"speed of boat in still water - rate of current"` a. 10miles per hour b.8.63 miles per hour c.3.16 miles per hour d.2.24 miles per hour

Let the speed of the water current be v.

total travel time = time to go upstream + time to return downstream to the starting point

Hence, 8 = time in hours = 6 / (4-v) + 6 / (4 +v) = 6*8/(16-v^2)

Hence, 16 - v^2 = 6, or v^2 = 10 or v = √10 miles / hour

The correct option is:   c.  3.16 miles per hour.

Step-by-step explanation:

Suppose, the rate of the current mph.

Speed of the boat is mph in still water.

So, speed of the boat in upstream mph and speed of the boat in downstream mph

We know,  

For upstream,  distance miles and speed mph

So, the time taken in upstream hours

For downstream,  distance miles and speed mph

So, the time taken in downstream hours

Now the total time taken for upstream and downstream is   hours, so the equation will be.....

So, the rate of the current is 3.16 miles per hour.

9 x 8 divided by (5-3)=36