Question 1143190: Danilo drove from his home in valenzuela a distance of 40 miles and then returned again on the same highway the round trip took 2hrs. His speed on the return trip was 30 miles per hour faster than his speed in going.What was his rate of speed on the trip from his home
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Danilo drove from his home in valenzuela a distance of 40 miles and then returned again on the same highway the round trip took 2hrs. His speed on the return trip was 30 miles per hour faster than his speed in going.What was his rate of speed on the trip from his home
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g = speed going
g+30 = return speed.
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Avg speed of the round-trip = 80/2 = 40 mi/hr
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Avg speed = 2*g*(g+30)/(g + g+30)
40 = (2g^2 + 60g)/(2g+30)
2g^2 + 60g = 80g + 1200
g^2 - 10g - 600 = 0
(g-30)*(g+20) = 0
g = 30 mi/hr ------ ignore the negative solution.
Return speed = 60 mi/hr
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PS There is no "rate of speed"
There's rate, and there's speed.
Answer by ikleyn(52800)  (Show Source):
You can put this solution on YOUR website! .
Let x = his rate on the trip from his home, in miles per hour (which is the unknown value under the question).
Then his rate on the way back is (x+30) mph.
The time spent for the trip "to there" is  hours.
The time spent for the trip back is  hours.
The total time is 2 hours, which gives you this "time" equation
+ = 2 hours.
To solve it, multiply both sides by x*(x+30). You will get
40*(x+30) + 40x = 2x*(x+30),
40x + 1200 + 40x = 2x^2 + 60x
2x^2 - 20x - 1200 = 0
x^2 - 10x - 600 = 0
(x-30)*(x+20) = 0
There are two roots, x= 30 and x= -20, but only positive x= 30 makes sense.
ANSWER. His rate "to there" is 30 mph.
CHECK.  +  = +  =   +  = 2 hours. ! Correct !
Solved.
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Using "time" equation is the STANDARD method of solving such problems.
It is simple, logical, straightforward and economic. Going in this way, you will not make a mistake - the logic of the method
prevents you of making mistakes.
From this lesson, learn on how to write, how to use and how to solve a "time" equation.
To see many other similar solved problems, look into the lessons
- Had a car move faster it would arrive sooner
- How far do you live from school?
- Earthquake waves
- Time equation: HOW TO use, HOW TO write and HOW TO solve it
in this site.
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