1 - To save fuel, to avoid air pollution and for good health two persons A and B ride bicycle for a distance of 12 km to reach their office. As the 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. Find the time taken by A and B to reach the office.
Answers
Given : two persons A and B ride bicycle for a distance of 12 km to reach their office.
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 = A km/hr
Speed of B = A + 2 km/Hr
Time = Distance / Speed
Time Taken by A = 12/A hr
Time Taken by B = 12/(A+2) hr
B takes 30 minutes less than that of A to reach the office.
30 minutes = 1/2 Hr
=> 12/(A + 2) = 12/A - 1/2
=> 12/A - 12/(A + 2) = 1/2
=> 24(1/A - 1/(A + 2) = 1
=> 24( A + 2 - A) /A(A + 2) = 1
=> 48 = A(A + 2)
=> A² + 2A - 48 = 0
=> A² + 8A - 6A - 48 = 0
=> A(A + 8) - 6(A + 8) = 0
=> (A - 6)(A + 8) = 0
=> A = 6 ,A = -8 neglected as speed can not be -ve
Speed of A = 6 km/hr
Speed of B = 8 km/hr
Time Taken by A = 12/6 = 2hr
Time taken by B = 12/8 = 3/2 hr = 1 hr 30 minutes
Time Taken by A to reach the office = 2 hr
Time Taken by B to reach the office = 1 hr 30 minutes
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