Answer:
x = 20
Step-by-step explanation:
The problem tells you the relationship between time, distance, and speed. Use the given relations to find the total journey time.
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equation
total time = Journey A time + Journey B time
total time = (distance A)/(speed A) + (distance B)/(speed B)
total time = 15/x +6/(x+4) = 1 . . . . . using the given values
solution
Multiplying by x(x+4) we have ...
15(x +4) +6(x) = (x)(x +4)
21x +60 = x² +4x
x² -17x -60 = 0 . . . . . rearrange to standard form
(x -20)(x +3) = 0 . . . . factor the equation
x = 20 or x = -3 . . . values of x that satisfy the equation
We know the speed must be positive, so x = -3 is an extraneous solution.
The value of x is 20 (km/h).
