SOLUTION: Mr. John traveled to a city 120 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 12 mph less than his speed going. If the total time f

Question 1027769: Mr. John traveled to a city 120 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 12 mph less than his speed going. If the total time for the round trip was 4 hours, at what rate of speed did he travel to the city? (Round your answer to the nearest tenth.)
Found 2 solutions by josmiceli, mananth:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = his time in hours going to the meeting
Let = his speed in mi/hr going to the meeting
---------------------
Equation for going to the meeting
(1)
Equation for returning from the meeting
(2)
----------------------------
(1)
and
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
Complete the square:
(2)
(2)
(2)
(2)
(2)
(2)
(2)
he traveled at 66.6 mi/hr to the city
---------------
check:
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
(2)
(2)
(2) hrs
OK
check the math
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Mr. John traveled to a city 120 miles from his home to attend a meeting.
speed be x mph
Due to car trouble, his average speed returning was 12 mph less than his speed going.
x-12 mph
If the total time for the round trip was 4 hours,
time going + time returning = 4
t=d/r

120(x-12) + 120x = 4x(x-12)

120x-1440+120x=4x^2-48x

4x^2-288x+1440=0
/4
x^2-72x+360=0
Find roots of the quadratic equation
a= 1 b= -72 c= 360

x1= ( 72 + sqrt( 5184 - -1440 )) / 2
x1=( 72 + 61.19 )/ 2
x1= 66.59

x2= ( -7 - sqrt( 49 - 20 ) / 2
x2=( 72 - 61.19 )/ 2
x2= 5.41
Going speed was 66.6 mph

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