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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = his time in hours going to the meeting
Let +s+ = his speed in mi/hr going to the meeting
---------------------
Equation for going to the meeting
(1) +120+=+s%2At+
Equation for returning from the meeting
(2) +120+=+%28+s+-+12+%29%2A%28+4+-+t+%29+
----------------------------
(1) +t+=+120%2Fs+
and
(2) +120+=+4s+-+48+-+s%2At+%2B+12t+
(2) +120+=+4s+-+48+%2B+t%2A%28+12+-+s+%29+
(2) +120+=+4s+-+48+%2B+%28+120%2Fs+%29%2A%28+12+-+s+%29+
(2) +120+%2B+48+=+4s+%2B+1440%2Fs+-+120+
(2) +120+-+48+%2B+120+=+4s+%2B+1440%2Fs%0D%0A%282%29+%7B%7B%7B+288+=+4s+%2B+1440%2Fs+
(2) +288s+=+4s%5E2+%2B+1440+
(2) +4s%5E2+-+288s+%2B+1440+=+0+
(2) +s%5E2+-72s+%2B+360+=+0+
Complete the square:
(2) +s%5E2+-72s+%2B+%28+-72%2F2%29%5E2+=+-360+%2B+%28+-72%2F2+%29%5E2+
(2) +s%5E2+-72s+%2B+1296+=+-360+%2B+1296+
(2) +s%5E2+-72s+%2B+1296+=+936+
(2) +%28+s+-+36+%29%5E2+=+30.594%5E2+
(2) +s+-+36+=+30.594+
(2) +s+=+30.594+%2B+36+
(2) +s+=+66.594+
he traveled at 66.6 mi/hr to the city
---------------
check:
(1) +120+=+s%2At+
(1) +120+=+66.594t+
(1) +t+=+1.802+ hrs
and
(2) +120+=+%28+s+-+12+%29%2A%28+4+-+t+%29+
(2) +120+=+%28+66.594+-+12+%29%2A%28+4+-+t+%29+
(2) +120+=+54.594%2A%28+4+-+t+%29+
(2) +120+=+218.376+-+54.594t+
(2) +218.376+-+120+=+54.594t+
(2) +54.594t+=+98.376+
(2) +t+=+1.802+ hrs
OK
check the math

Answer by mananth(16946) About Me  (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%2Fx%2B120%2F%28x-12%29=4

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