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
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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):
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.