To save fuel , to avoid air pollution and for good health two persons A and B ride bicycle for a distance of 12km to reach their office. As the cycling speed of B is 2km/h more than that of A ,B takes 30 minutes less than that of A to reach the office. Find the time taken by A and B to reach the office
Answers
Given : A and B ride bicycle for a distance of 12km to reach their office. As cycling speed of B is 2 km/h more than that of A, B takes 30 minutes less than that of A to reach the office.
To find : the time taken by A and B to reach the office
Solution:
Distance of Office =12 km
Speed of A = S km/hr
Speed of B = S + 2 km/hr
Time taken by A = 12/S hr
Time Taken by B = 12/(S + 2) hr
B takes 30 minutes less than that of A to reach the office.
30 minutes = 1/2 hr
=>12/(S + 2) = 12/S - 1/2
=> 12*2S = 12*2(S + 2) - S(S + 2)
=> 24S = 24S + 48 - S² - 2S
=> S² + 2S - 48 = 0
=> S² + 8S - 6S - 48 = 0
=> S(S + 8) - 6(S + 8) = 0
=> (S - 6) (S + 8) = 0
=> S = 6 , S = - 6
Speed of A = 6 km/hr
Speed of B = 8 km/hr
Time taken by A = 12/6 = 2 hr
Time taken by B = 12/8 = 1.5 hr
Time taken by A and B to reach the office are 2 hr & 1.5 hr respectively
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