It takes 40 min for a bus to cover 36 miles. a car travels 1.4 times faster. when will they meet if they started 36 miles apart and simultaneously move towards each other? if they were moving in opposite directions the biker's speed is mph and the walker's speed is mph

we know that

speed=distance/time

It takes 40 min for a bus to cover 36 miles

then

speed of the bus=distance/time> 36/40> 0.9 miles/min

speed of the car=1.4*speed of the bus> 1.4*0.9> 1.26 miles/min

For time=t

bus

t=distance/speed> t=x/0.9> equation 1

car

t=distance/speed> t=(36-x)/1.26> equation 2

equate equation 1 and equation 2

x/0.9=(36-x)/1.26> 1.26x=0.9*(36-x)> 1.26x=32.4-0.9x

1.26x+0.9x=32.4> x=32.4/2.16> x=15 miles

equation 1

t=x/0.9> 15/0.9> t=16.67 min

the answer is

they will meet at the time 16.67 minutes

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.