A boat travels at 16 mph in still water It takes the same am

A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15 mi downstream as to go 9 mi upstream. Find the speed of the current. Flying at a constant speed, a plane can travel 800 mi with the wind in the same amount of time it can fly 650 mi against the wind. If the wind blows at 30 mph, what is the speed of the plane?

Solution

23).

Let x mph is the speed of current
Given speed of the boat in still water = 16 mph

then downstream speed = (16 + x) mph

and upstream speed = (16 - x) mph

then use the distance formula:

for downstream t = 15 / (16 + x)

for upstream t= 9 / (16 - x)


in both condition its travels in same time, then
15 / (16 + x) = 9 / (16 - x)

5 / (16 + x) = 3 / (16 - x)

3(16 + x) = 5 (16 - x)

48 + 3x = 80 - 5x

3x + 5x = 80 - 48 = 32

8x = 32

x = 32/8 = 4

speed of current = 4 mph

28.)

Let x mph is the speed of plane
Given wind speed = 30 mph

then plane speed with the wind = (x + 30) mph

and plane speed against the wind = (x - 30) mph

then use the distance formula:

time taken with the wind = 800 / (x + 30)

time taken against the wind = 650 / (x - 30)

in both condition its travels in same time, then

800 / (x + 30) = 650 / (x - 30)

16 / (x + 30) = 13 / (x - 30)

16(x - 30) = 13(x + 30)

16x - 480 = 13x + 390

16x - 13x = 480 + 390

3x = 870

x = 870/3 = 290

speed of plane = 290 mph