David drives from his home to the airport to catch a flight. He drives

Question

David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15 miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles is the airport from his home?

A) 140

B) 175

C) 210

D) 245

E) 280

A) 140
B) 175
C) 210
D) 245
E) 280

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Kinshook · Answer

Given: David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15 miles per hour for the rest of the way to the airport and arrives 30 minutes early.

Asked: How many miles is the airport from his home?

Let distance from home to airport be x miles and time taken to reach the airport on time be t hours.

He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. 
x = 35 + 35(t-1+1)= 35(t+1)

He increases his speed by 15 miles per hour for the rest of the way to the airport and arrives 30 minutes early. 
x = 35 + 50(t-1-.5) = 35 + 50t -75= 50t - 40

x = 35t + 35 = 50t - 40
t = 75/15 = 5 hours

x = 35(5+1) = 210 miles

IMO C

zhanbo · Answer

Let m be the miles from his home to the airport.
Let x = m - 35 
We have
x/35 - x/50 = 3/2
10x-7x=3 / 2 * 350
x=175

m = 210

The answer is thus  (C) .

GmatPoint · Answer

Since the distance is constant in this case, let the total distance be D.

Also, let the correct time of arrival be T.

For 35 miles per hour,
D/35 = T + 1
D = 35*T + 35
Since he has driven for 1 hour at 35 miles per second, the remaining distance will be D - 35 miles. Also, 1 hour has already lapsed.

If he increased his speed by 15 miles, his speed would become 50.
Time left = T - 1
Since he will reach 30 minutes early, the time taken to reach after travelling 35 miles = T - 1 - 1/2
Thus, time taken in this case = T - 3/2

For 50 miles per hour,
D - 35 = 50*(T - 3/2)
35*T + 35 - 35 = 50*T - 75
15T = 75
T = 5 hours

Thus, D = 35*5 +35 = 210

Thus, the correct option is C.

ThatDudeKnows · Answer

Rather than setting up algebra, I'd just go with Plugging In The Answers. I like trying B and D.

Going from 1 hour late to 0.5 hour early is a difference of 1.5 hours between the two methods.

B: 175 total miles. At 35mph, it would have taken 5 hours. Once he did 35 miles in the first hour, there would be 140 to go. At 50mph, that's 2.8 hours. Total time 3.8 hours, which is 1.2 hours faster than doing all of it at 35mph. That's not 1.5 hours. Wrong.

D. 245 total miles. At 35mph, it would have taken 7 hours. Once he did 35 miles in the first hour, there would be 210 to go. At 50mph, that's 4.2 hours. Total time 5.2 hours, which is 1.8 hours faster than doing all of it at 35mph. That's not 1.5 hours. Wrong.

At this point, we do NOT need to try the other three answer choices. We need something between B and D.

Answer choice C.

Adit_ · Answer

I dont really understand, it says he drove 35 miles in the first hour and that he will be 1 hour late if he continues so, so it is the same as "he drives at 35 mph and if he drives at this speed he will be 1 hr late"?

David drives from his home to the airport to catch a flight. He drives

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David drives from his home to the airport to catch a flight. He drives

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