A-town and b-ville are connected by a straight, 420-mile road. at noon, atu left a-town for b-ville, and brek left b-ville for a-town. if atu travels at 56 miles per hour and brek travels at 49 miles per hour, how many miles apart will atu and brek be 1 hour before they meet?

Let x be the number of hours it will take for Atu and Brek to meet and cover the total distance of 420. The distance covered is the product of the speed and time. Thus,
 
56x + 49x = 420
105x = 420

The value of x from the derived equation is equal to 4 hours.

One hour less than the number of hours calculated above is 3 hours. The distances covered are calculated below.

Atu = (56 mph)(3 hours)  = 168 miles
Brek = (49 mph)(3 hours) = 147 miles

The total distance covered is equal to 315 miles.

Subtracting this distance from the given total distance.
  difference = 420 miles - 315 miles = 105 miles

ANSWER: 105 miles

i) 0.63

ii) 0.37

iii) 0.37

iv) 0.77

v) 0.51

Step-by-step explanation:

Total resistance value = 108

A = high shock resistance

B = high scratch resistance

when a disk is selected at random

i) P(A) = P ( high shock resistance )

          = ( 55 + 13 ) / 108

          = 68/108 =  17/27   = 0.63

ii) P( B ) = P ( high scratch resistance )

            = ( 10 + 30 ) / 108

            = 40 / 108 = 10/27  = 0.37

iii) P(A') = 1 - P(A)

            = 1 - 17/27 = 10/27  = 0.37

iv) P( A U B ) = P(A) + P(B) - P( A n B )

                    = 0.63 + 0.37 - 0.233

                    = 0.766 ≈ 0.77

v) P( A' U B ) = P(A') + P(B) - P(A n B )

                     = 0.37 + 0.37 - 0.233

                     = 0.507 ≈ 0.51