On the first part of a trip to carmel traveling on the freeway, marge averaged 70 mph. on the rest of the trip, which was 25 mi longer than the first part, she averaged 60 mph. find the total distance to carmel if the second part of the trip took 30 minutes more than the first part.

95 miles

Step-by-step explanation:

Let the distance traveled in first part be x

Speed = 70 mph

So, Time =

We are given that  On the rest of the trip, which was 25 mi longer than the first part, she averaged 60 mph.

So, distance in second part = x+25

Speed = 60

So, Time =

Now we are given that he second part of the trip took 30 minutes more than the first part.

So, total distance = distance in first part+ distance in second part = x+x+25=35+35+25= 95

Hence the total distance is 95 miles

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.

answer: x=60