Problema Solution
Meg rowed her boat upstream a distance of 32 miles and then rowed back to the starting point. the total time of the trip was 12 hours. if the rate of the current was 2 mph, find the average speed of the boat relative to the water.
Answer provided by our tutors
distance = speed * time
speed = distance / time
we interpret "the average speed of the boat relative to the water" to be equivalent to "the speed of the boat if in still water"
let 'x' represent the speed of boat with no current, then 'x-2' represents the speed upstream and 'x+2' represents the speed downstream
let 't' represent the time upstream, then '12-t' represents the time downstream
32 = (x-2)t, so t = 32/(x-2)
32 = (x+2)(12-t)
substituting 't = 32/(x-2)' into "32 = (x+2)(12-t)":
32 = (x+2)(12-(32/(x-2)))
solving for 'x' we have a positive value of x=6
the average speed of the boat with no current is 6mph