Deb normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Deb averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?

(A) 135
(B) 105
(C) 95
(D) 75
(E) 45


Work place is 30 miles away (3/4*40) when Deb drives.
When Deb bikes the distance is 30*80/100 = 24 miles
If she travels at an average of 12 mph it will take 120 minutes
If she travels at an average of 16 mph it will take 90 minutes

For that to happen she will have to start between 75 and 45 minutes earlier than she used to. I dont know which answer is feasible as both D and E are seeming to be all right. Yet, since we dont want her to be late so to make sure that she reaches on time 75 is better, as it is always safe.
How muchever is her biking speed she reaches the office if she starts 75 mins earlier. ( worst case scenario??) ... Heh

D it is. The question asks to ensure that Deb arrives on time, so we have to go for the worst case value like Ajith suggested.