the potomac river has a 3 mph current a tour boat travels 40

the potomac river has a 3 mph current. a tour boat travels 40 miles up river and returns in a total time of 10 hr. find the speed of the tour boat in still water.

Solution

speed of current = 3 mph

Let speed of boat be s mph

(distance traveled upriver)/(rate going upriver)
+ (distance traveled downriver)/(rate going downriver) = 10 hrs

So, 40/( s -3) +40/(s +3) = 10

4*2s/(s^2 - 9) =1

8s = s^2 -9

s^2 - 8s -9 =0

s^2 -9s +s -9 =0

s( s-9) +1(s -9) =0

(s +1)(s -9) =0

s = -1 , 9 neglect -ve speed

So, speed of boat is = 9 mph