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Admissions Success Stories Speed/time

This topic has 2 expert replies and 0 member replies

Speed/time

Post Wed Aug 01, 2018 2:54 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



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

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Top Reply
Post Wed Aug 01, 2018 3:25 am
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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Post Fri Aug 10, 2018 5:36 pm
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 45 minutes = ¾ hour, the distance between her house and work is 40 x ¾ = 30 miles. This is her driving route. Since her biking route is 20% shorter, her biking route is 0.8 x 30 = 24 miles.

To guarantee she will arrive at the same time as when she drives, we have to assume she bikes at her slow rate of 12 m/h. Thus it will take her 24/12 = 2 hours, or 120 minutes, to bike to work. So she has to leave 120 - 45 = 75 minutes earlier.

Answer: D

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