George's home is 20 miles from his place of work. One day as he is dri

Question

George's home is 20 miles from his place of work. One day as he is driving home from work, his car breaks down when he is 5 miles from work. He starts walking toward his home at an average rate of 4 miles per hour. If d represents his distance from home, in miles, and t represents the time, in hours, that he has been walking, which of the following gives d in terms of t ?

A.​ d = 15 - 4t​
B.​ d = 20 - 4t​
C.​ d = 4t - 15​
D.​ d = 4t - 20​
E.​ d = 4t + 5

Source: Skills Insight

Bunuel · Accepted Answer

George's home is 20 miles from his place of work. One day as he is driving home from work, his car breaks down when he is 5 miles from work. He starts walking toward his home at an average rate of 4 miles per hour. If d represents his distance from home, in miles, and t represents the time, in hours, that he has been walking, which of the following gives d in terms of t ?

A. d = 15 - 4t
B. d = 20 - 4t
C. d = 4t - 15
D. d = 4t - 20
E. d = 4t + 5

The total distance between work and home is 20 miles. George's car breaks down 5 miles from work, leaving him 15 miles from home.

If George walks at a rate of 4 miles per hour, then after t hours, he covers 4t miles. Therefore, the remaining distance from home, d, after t hours is d = 15 - 4t miles.

For example:

If t = 0 (he hasn’t started walking), d = 15 miles from home. 
 If t = 2 hours, d = 15 - 4(2) = 7 miles from home. 
 If t = 3.75 hours (3 hours and 45 minutes), d = 15 - 4(3.75) = 0 miles from home, meaning he has reached home.

Answer: A

avggmatstudent23 · Answer

total distance = 20
distance left = d = 20-5 = 15
rate of walking = 4 mi/h

d = 4t - 15 (C)

nbrn226 · Answer

20
h ------------------------- w
 d | 4t | 5

d+4t+5=20
d=15-4t

A

FALSEnine9 · Answer

I think the question becomes mind boggling once you arrive pretty quickly at 15 = 4t.
But the trick is to realize that the question asks for relationship between distance d and time t at any point during the journey, for which distance will be arrived at by subtracting distance travelled until that point in time t from total 15 miles.

Hence, equation becomes d = 15-4t , where t is time elapsed at any point in time during the walk, 4t is the distanced covered in time t, and d is the remaining distance from home from total 15 miles.
Hope it's clear.

CrackverbalGMAT · Answer

George's home is 20 miles from his place of work. One day as he is driving home from work, his car breaks down when he is 5 miles from work. He starts walking toward his home at an average rate of 4 miles per hour. If d represents his distance from home, in miles, and t represents the time, in hours, that he has been walking, which of the following gives d in terms of t ?

A.​ d = 15 - 4t​
B.​ d = 20 - 4t​
C.​ d = 4t - 15​
D.​ d = 4t - 20​
E.​ d = 4t + 5

You can either solve this question by plugin approach or by forming an equation connecting d and t, where d represents his distance from home and t represents his walking time in hours.

#1  : Plugin approach
 
It's given that the distance between George's home and his workplace is 20 miles. When his car breaks down he is 5 miles away from work. That means he needs to walk 15 miles to reach home.

So we can say that the value of 'd' should be 15 miles when t =0.

Why don't we plugin these values and cross-check how many options will satisfy this condition? Let's try it out

A.​ d = 15 - 4t​ ==> t =0, d = 15
B.​ d = 20 - 4t​ ==> t =0, d = 20 Eliminated
C.​ d = 4t - 15​ ==> t =0, d = -15 Eliminated
D.​ d = 4t - 20​ ==> t =0, d = -20 Eliminated
E.​ d = 4t + 5 ==> t =0, d = 5 Eliminated

The above condition is only satisfied in Option A. Hence, Option A is the correct answer.

#2  Forming the equation

We know that George needs to walk 15 miles to reach home from the breakdown point. He walks at an average speed of 4 miles /hr.

Distance covered by George by walking 't' hours = 4t

The remaining distance left to reach home i.e d = 15 -4t

Option A is the correct answer.

Thanks,
Clifin Francis,
GMAT Mentor

saynchalk · Answer

Confusing wording, had to ignore a lot of logical issues and just assume things are as they are. Still, answer in 30 secs.

bumpbot · Answer

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George's home is 20 miles from his place of work. One day as he is dri

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