Question
A motorboat moves downstream at 30 km/h over a distance
of 480 km. After completing half the distance, the stream’s speed becomes 50% higher than before. Because of this, the boat reaches 30 minutes earlier than the usual time. Find the original speed of the stream.Solution
ATQ, Let the original speed of the stream be x km/h. Original time = 480/30 = 16 hours Time for first half = 16/2 = 8 hours New total time = 16 − 0.5 = 15.5 hours Time for second half = 15.5 − 8 = 7.5 hours Speed in second half = 240/7.5 = 32 km/h Net increase = 32 − 30 = 2 km/h So, 1.5x − x = 2 0.5x = 2 x = 4
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 37x² - 172x + 135 = 0
Equation 2: 29y² - 132y + ...
I. p2 - 19p + 88 = 0Â Â
II. q2 - 48q + 576 = 0
For what real value(s) of k does the quadratic equation - x² − (k + 3)x + 2k = 0, have equal real roots?
I. x2 – 12x + 32 = 0
II. y2 + y - 20 = 0
I. 195x² - 46x - 21 = 0
II. 209y² + 13y - 12 = 0
I. x² - (16)2 = 0
II. 2y - 14 = 0
Solve for x: |2x − 5| + |x + 1| ≤ 10.
I. 9x2 + 45x + 26 = 0
II. 7y2 – 59y − 36 = 0
Roots of the quadratic equation 2x2 + x – 528 = 0 is
