Sam and Mark run towards each other starting from P and respectively with respective speeds of 4 kmph and 6 kamph. After meeting other, to reach Q if Sam takes 9.1 hours less than the square of magnitude of the total time (in hours) taken by Mark to reach P, find the distance between p and q
Answers
Given : Sam and Mark run towards each other starting from P and Q respectively with respective speeds of 4 kmph and 6 kmph. After meeting each other, to reach Q if Sam takes 9.1 hours less than the square of magnitude of the total time (in hours) taken by Mark to reach P,
To find : the distance between p and q
Solution:
Let say Distance = 120D km
Time taken to Meet each other = 120D/ (4 + 6) = 12D hrs
Distance covered by Sam = 4 * 12D = 48D km
Distance covered by Mark = 6 * 12D = 72 D km
Total time taken by Mark = 120D /6 = 20D hrs
Time taken by Sam to reach Q after meeting = 72D/4 = 18D hrs
18D + 9.1 = (20D )²
=> 18D + 9.1 = 400D²
=> 400D² - 18D - 9.1 = 0
=> 400D² -70D + 52D - 9.1 = 0
=> 10D(40D - 7) + 1.3(40D - 7) = 0
=> D = 7/40 is only positive solution
Distance = 120D = 120 * 7/40 = 21 km
distance between p and q is 21 km
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