SOLUTION: Junior drove his rig on Interstate 10 from San Antonio and El Paso. At the halfway point he noticed that he had been averaging 80 mph, while his company requires his average speed

Question 824528: Junior drove his rig on Interstate 10 from San Antonio and El Paso. At the halfway point he noticed that he had been averaging 80 mph, while his company requires his average speed to be 60 mph. What must be speed for the last half of the trip so that he will average 60 mph for the entire trip. Distance doesn't matter.
Found 2 solutions by TimothyLamb, MathTherapy:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
---
s = d / t
t = d / s
D = half trip distance
---
first half (a):
t = d / s
ta = D/80
---
second half (b):
t = d / s
tb = D/x
where x is the unknown speed for the second half
---
whole trip:
s = d / t
60 = 2D / (ta + tb)
60 = 2D / (D/80 + D/x)
60(D/80 + D/x) = 2D
60(xD/80x + 80D/80x) = 2D
(60D/80x)(x + 80) = 2D
(60/80x)(x + 80) = 2
x + 80 = 2*(80/60)x
x + 80 = (2.666666)x
(2.666666)x - x = 80
(1.666666)x = 80
x = 80/1.666666
x = 48.0
---
answer:
the speed for the last half of the trip must be: 48 mph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

Junior drove his rig on Interstate 10 from San Antonio and El Paso. At the halfway point he noticed that he had been averaging 80 mph, while his company requires his average speed to be 60 mph. What must be speed for the last half of the trip so that he will average 60 mph for the entire trip. Distance doesn't matter.

Let distance be D, and speed on last � of trip, S
Then time he took to travel 1st � of the distance = �D/80, or
Time 2nd � of trip should take = �D/S, or � S, or
Average speed =
Therefore, 60 = D �
60 = D � ____ = *

60(DS + 80D) = 160DS ------ Cross-multiplying
60DS + 4,800D = 160DS
D(60S + 4,800) = D(160S) ------ Factoring out GCF, D
60S + 4,800 = 160S
60S � 160S = - 4,800
� 100S = - 4,800
S, or speed on 2nd � of journey should be: , or mph
You can do the check!!
Send comments, �thank-yous,� and inquiries to �D� at MathMadEzy@aol.com.
Further help is available, online or in-person,for a fee, obviously.
For FREE info and answers to questions about the ASVAB exam, the NYS 3 � 8 city/state wide exams,
GENERAL MATH QUESTIONS, MATH HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra,
Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE, GRE, CLEP,
and the GED, you can visit: http://asvabstudyzone.freeforums.net/.
RELATED QUESTIONS
Junior drove his rig on the Interstate 10 from San Antonio to El Paso. At the halfway... (answered by stanbon,ankor@dixie-net.com)
Junior drove his rig on Interstate 10 prom San Antonio to El Paso. At the halfway point... (answered by checkley71)
You are driving from Houston to San Antonio on Interstate 10. You travel half the... (answered by richwmiller,Deina)
Antonio drove 26 miles north, and then drives west. At the end of his drive, it is... (answered by Alan3354,josgarithmetic)
Jacob drove from St. Petersburg, Florida to Phoenix, Arizona, stopping in Baton Rouge,... (answered by stanbon)
You drive on Interstate 10 from San Antonio to Houston, half the time at 50 km/h and the... (answered by josmiceli)
Richard drove his rig at �x� mph for 3 hours, then increased his speed to (x + 15) mph... (answered by funmath)
Travel problems I just don't understand. Richard drove his rig at 'x' mph for 3 hours,... (answered by jejess)
Richard drove his rig at �x� mph for 3 hours, then increased his speed to (x + 15) mph... (answered by drj)