One boat travelling 15 mph goes 47 miles downstream in the same amount of time that another boat going 20 mph goes 40 miles upstream. how fast is the current in mph? (round your answer to the nearest tenth of miles per hour and enter only the numerical part

  3.9 mi/h

Step-by-step explanation:

We assume that the given speeds are the speeds of the boats relative to the water. If c is the speed of the current, we have ...

  time = distance/speed

  47/(15 +c) = 40/(20 -c)

  47(20 -c) = 40(15 +c) . . . . . . multiply by (20-c)(15+c)

  940 -600 = 40c +47c . . . . . add 47c-600

  340 = 87c . . . . . . . . . . . . . . . simplify; next divide by 87

  c = 340/87 ≈ 3.9080 . . . . mi/h

The speed of the current is about 3.9 mi/h.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

the answer would be 484

step-by-step explanation:

just multiply 0.484 times 1,000 (formula)