.
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.