Jamie recently drove to visit her parents who live 189 miles

Jamie recently drove to visit her parents who live

189

miles away. On her way there her average speed was

16

miles per hour faster than on her way home (she ran into some bad weather). If Jamie spent a total of

6

hours driving, find the two rates.

Solution

Distance = 189 miles

Let\'s the speed coming home is x miles per hour so, the speed to go to parents must be (x+16) miles per hour.

Time to reach back home = distanace/speed = (189/x) hours

Time to go the parents = distance/speed = {189/(x+16)} hours.

Since the total time for the return journey is given 6 hours so,

time to go to the parents + time to be back home = 6 hours

{189/(x+16)} + {189/x} = 6

189 [ 1/(x+16) + 1/x] = 6   (dividing both sides by 3)

63[ 1/(x+16) + 1/x] = 2

63[(2x+16)/(x(x+16)] = 2 (Taking 2 out as common factor)

63*2[(x+8)/(x²+16x)] = 2 (dividing both sides 2)

63[(x+8)/(x² + 16x)] = 1

63(x+8) = 1(x² + 16x)

63x + 504 = x² + 16x

x² - 47x - 504 = 0

a=1, b=-47, c=-504

x = [-b±(b²-4ac)] / 2a
= [47±{(-47)²-4*1*(504)}]/2*1
= [47±{2209+2016}]/2
= [47±4225]/2
= [47±65]/2
= [47+65]/2 , [47-65]/2
= 56, -9 (speed cannot be negative so, -9 is rejected)

Thus, the speed (rate) to the parents is (x+16) = 56+16 = 72 miles per hour and speed to home = x = 56 miles per hour