c = speed of current p = paddling speed in still water
Against current: speed = p-c (start with paddling speed and subtract off current's speed) speed = 2 (given) p-c = 2 p = 2+c
With the current speed = p+c (now the current is speeding things up, so we add on c) speed = 3 (given) p+c = 3 2+c+c = 3 ... plug in p = 2+c; solve for c 2+2c = 3 2+2c-2 = 3-2 2c = 1 c = 1/2 c = 0.5
Since c = 0.5, we can use this to find p p = 2+c p = 2+0.5 p = 2.5
So, The speed of the river current is 0.5 mph Rita's paddling speed in still water is 2.5 mph
Terms to know: headwind = wind that slows the plane down (wind is coming from the head of the plane flowing in the opposite direction of the plane's intended direction) tailwind = wind that speeds the plane up (wind is coming from the tail of the plane flowing in the same direction of the plane's intended direction)
d = distance = 255 miles p = speed of plane in still air w = speed of wind
Against the wind (headwind), the plane travels 1.7 hours at some speed p-w. We start with the plane's speed in still air (p) and subtract off the wind speed because the wind is slowing the plane down. So the first equation is (p-w)*1.7 = 255 since the plane travels 255 miles I'm using the formula d = r*t d = distance r = rate or speed t = time
Divide both sides of (p-w)*1.7 = 255 by 1.7 and we get p-w = 150 Then add w to both sides and we have p = 150+w
Similarly, the second equation is (p+w)*1.5 = 255 since the tailwind speeds the plane up from p to p+w, the time is 1.5 hrs and the distance is the same (255 mi)
Plug the equation p = 150+w into the second equation (p+w)*1.5 = 255 (150+w+w)*1.5 = 255 (150+2w)*1.5 = 255 150*1.5+2w*1.5 = 255 225+3w = 255 225+3w-225 = 255-225 3w = 30 3w/3 = 30/3 w = 10
Use w = 10 to find p p = 150+w p = 150+10 p = 160
So, wind speed = 10 mph speed of plane in still air = 160 mph
