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

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Joined: 02 Nov 2018
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David drives from his home to the airport to catch a flight. He drives  [#permalink]

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19 Mar 2019, 07:22
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Difficulty:

65% (hard)

Question Stats:

56% (03:31) correct 44% (03:04) wrong based on 25 sessions

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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
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David drives from his home to the airport to catch a flight. He drives  [#permalink]

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19 Mar 2019, 07:28
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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

$$Speed = \frac{Distance}{Time}$$

Initial speed = 35 miles per hour
Increased speed = 35+15 = 50 miles per hour

Let total distance = 35+D where D is the distance travelled at increased speed

$$Time = \frac{Distance}{Speed}$$

Time taken to travel D at speed of 35 miles per hour = D/35

Time taken to travel D at speed of 50 miles per hour = D/50

Given, (D/35) - 1 = (D/50) + (1/2)

i.e. (D/35) - (D/50) = 1+(1/2)

i.e. 3D / 350 = 3/2

i.e. D = 175

i.e. Total Distance = 35+175 = 210

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David drives from his home to the airport to catch a flight. He drives   [#permalink] 19 Mar 2019, 07:28
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