vaibhav101 wrote:Deb normally drives to work in 45 minutes at an average speed of 40 m/h. This week 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 & 16 m/h when biking, how many minutes earlier will she need to leave in the morning in order to arrive at the same time as when she drives?
A 135
B 105
C 95
D 75
E 45
Since Deb drives for 3/4 of an hour at a rate of 40 mph, the driving distance to work = rt = (40)(3/4) = 30 miles.
Since the biking distance is 20% less than the driving distance, the biking distance = 30 - (1/5)(30) = 24 miles.
To guarantee an on-time arrival at even the least possible biking speed -- 12 mph -- the time required to travel 24 miles = d/r = 24/12 = 2 hours.
Since the time to work increases from 3/4 hour to 2 hours -- a difference of 1.25 hours -- Deb must leave 75 minutes early to guarantee an on-time arrival.
The correct answer is
D.
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