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Joined: 10 Apr 2015
Posts: 6218
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Today Dave drove from home to work at twice his regular speed and arri
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19 Jul 2022, 06:24
19 Jul 2022, 06:24
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Today Dave drove from home to work at twice his regular speed and arrived at work 16 minutes earlier than he regularly arrives. If Dave regularly drives at a constant speed of 40 miles per hour, what is the distance, in miles, from Dave’s home to work?
(A) 16/3
(B) 32/3
(C) 40/3
(D) 64/3
(E) 80/3
(A) 16/3
(B) 32/3
(C) 40/3
(D) 64/3
(E) 80/3
Intern
Joined: 28 May 2022
Posts: 4
Given Kudos: 0
GMAT 1: 650 Q48 V30
Today Dave drove from home to work at twice his regular speed and arri
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20 Jul 2022, 03:48
20 Jul 2022, 03:48
2
Let's use the DST formula
speed = distance / time
Let's take distance as d and time as t (t1 for general scenario, t2 when speed doubled)
Regular situation Todd's speed is 40miles per hour
40 = d / t1
d = 40*t1 ------------ 1
Now when the speed doubles the time (t1) is reduced by 16mins. New speed is 80 miles per hour
Convert 16mins into hours (16/60)
80 = d / (t1 - (16/60)) ----------- 2
substitute 1 in 2
80 = (40*t1) / (t1 - (16/60))
solving this we get
t1 = 8/15 hours
substitute this in 1
d = 40 * 8/15
d = 64/3
Hence Option D
speed = distance / time
Let's take distance as d and time as t (t1 for general scenario, t2 when speed doubled)
Regular situation Todd's speed is 40miles per hour
40 = d / t1
d = 40*t1 ------------ 1
Now when the speed doubles the time (t1) is reduced by 16mins. New speed is 80 miles per hour
Convert 16mins into hours (16/60)
80 = d / (t1 - (16/60)) ----------- 2
substitute 1 in 2
80 = (40*t1) / (t1 - (16/60))
solving this we get
t1 = 8/15 hours
substitute this in 1
d = 40 * 8/15
d = 64/3
Hence Option D
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Today Dave drove from home to work at twice his regular speed and arri
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20 Jul 2022, 06:18
20 Jul 2022, 06:18
1
GreenlightTestPrep wrote:
Today Dave drove from home to work at twice his regular speed and arrived at work 16 minutes earlier than he regularly arrives. If Dave regularly drives at a constant speed of 40 miles per hour, what is the distance, in miles, from Dave’s home to work?
(A) 16/3
(B) 32/3
(C) 40/3
(D) 64/3
(E) 80/3
(A) 16/3
(B) 32/3
(C) 40/3
(D) 64/3
(E) 80/3
Dave's regular driving speed = 40 mph
Dave's driving speed TODAY = 80 mph
Let d = the distance from Dave's home to work
Dave arrived at work 16 minutes earlier than he regularly arrives.
We can write: regular travel time in hours - 16/60 hours = today's travel time in hours
time = distance/rate, which means we can write: d/40 - 16/60 hours = d/80
Rewrite each fraction with denominator 240 to get: 6d/240 - 64/240 hours = 3d/240
Multiply both sides of the equation by 240 to get: 6d - 64 = 3d
Subtract 6d from both sides: -64 = -3d
Divide both sides by -3 to get: 64/3 = d
Answer: D
