SOLUTION: A motorist drove a distance of 90km at a constant speed for the first 40 km and then drove 20 km faster for the rest of the journey. If the whole journey took him one hour,his aver

Question 1158139: A motorist drove a distance of 90km at a constant speed for the first 40 km and then drove 20 km faster for the rest of the journey. If the whole journey took him one hour,his average speed for the first 40 km was
Answer by ikleyn(52799) (Show Source): You can put this solution on YOUR website!
.


Let x (kilometres per hour) be the average speed for the first 40 km.

Then the remaining 90-40 = 50 milometers his average speed was (x+20) kilometres per hour.


The traveling time for the first 40 kilometres was    hours.

The traveling time for the remaining 50 kilometres was    hours.


The total time was 1 hour

     +  = 1  hour.


It is your "time" equation.


To solve it, multiply both sides by x*(x+20). you will get then

    40*(x+20) + 50x = x*(x+20).


Simplify and solve

    40x + 800 + 50x = x^2 + 20x

    x^2 - 70x - 800 = 0

    x =  =  = .


Of the two roots, only positive value x =  = 80 is the solution to the problem.


ANSWER.  The average speed for the first 40 km was 80 km/h.

Solved.

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Using   "time" equation is a STANDARD method of solving such problems.
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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