Question

26.
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,​

Answer 1

Answer:

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

Proof :

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