Three friends A, B and C started their journey at 08:00 am from the points (2, 31),(3, 51),
and (6, 0) respectively. A followed the path along the curve 3x^2 +2x+15 and B followed the path along the curve 2x^2 + 10x + 3. They all meet at 11:00 am at a point P whose x coordinate is greater than 4. If C followed a straight-line path, and one unit is equal to 1 km then what was the speed of C? a. 31.26 km/hr
b. 32 km/hr
c. 45 km/hr
d. 45.5 km/hr
e. 43km/hr
f. 34km/hr
Answers
Given : Three friends A, B and C started their journey at 08:00 am from the points (2, 31),(3, 51), and (6, 0) respectively.
A followed the path along the curve 3x^2 +2x+15
B followed the path along the curve 2x^2 + 10x + 3.
They all meet at 11:00 am at a point P whose x coordinate is greater than 4
C followed a straight-line path, and one unit is equal to 1 km
To Find : speed of C
a. 31.26 km/hr
b. 32 km/hr
c. 45 km/hr
d. 45.5 km/hr
e. 43km/hr
f. 34km/hr
Solution:
3x² + 2x + 15 = 2x² + 10x + 3
=> x² - 8x + 12 = 0
=> x² - 6x - 2x + 12 =0
=> (x - 6)(x - 2) = 0
=> x = 6 , 2
x coordinate is greater than 4
=> x = 6
3x² + 2x + 15 at x = 6 is 3(6)² + 2(6) + 15 = 108 + 12 + 15 = 135
2x² + 10x + 3 at x = 6 is 2(6)² + 10(6) + 3 = 72 + 60 + 3 = 135
point is ( 6 , 135)
C started (6, 0)
Hence Distance covered by C = 135 unit
= 135 km
Started at 8 and meet at 11
Hence 3 hrs
Speed of C = 135 /3 = 45 km/hr
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Answer:
speed=45 km/hr
option c is correct