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Ron drives from his home to the airport to catch a flight.

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Intern
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Joined: 08 Mar 2019
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Ron drives from his home to the airport to catch a flight.  [#permalink]

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New post 08 Mar 2019, 04:38
1
00:00
A
B
C
D
E

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Question Stats:

58% (02:32) correct 42% (02:32) wrong based on 26 sessions

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Ron 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
Manager
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Re: Ron drives from his home to the airport to catch a flight.  [#permalink]

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New post 08 Mar 2019, 05:06
2
Distance travelled by Ron in the first hour = 35 miles
Speed of Ron = 35mph
Let the time be "t"
Now he will be late if by one hour if he drives at 35mph and 30 minutes early if he drives at (35+15) mph

Therefore 35(t+1) = 50(t-0.5)
35t + 35 = 50t - 25
T= 4
Distance = 35t +35 = 175
Distance travelled in the first hour= 35 miles
Total distance= 175+35 = 210 miles.

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Re: Ron drives from his home to the airport to catch a flight.  [#permalink]

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New post 08 Mar 2019, 05:21
1
Instead of spending time thinking about how one can set up an equation to solve the problem, one can simply start checking the answer choices. Quickly checking, we know that neither choice (A) or choice (B) but (C) We can verify as follows. After 1 hour at 35 mph, David has 175 miles left. This then takes him 3.5 hours at 50 mph. But 210/35 = 6 hours. Since 1+3.5 = 4.5 hours is 1.5 hours less than 6, so answer is c .
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Director
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Re: Ron drives from his home to the airport to catch a flight.  [#permalink]

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New post 08 Mar 2019, 09:30
1
Let D is the total distance, t2 is the time of part 2 of the journey, and T is the total estimated time. fit the data into a table.

D = distance 1 + distance 2 = 35 + (D-35) = 35 + 50t2 = 35(T+1)
35 + 50t2 = 35T + 35
10t2 = 7T ---> (1)

actual total time = time 1 + time 2
T - 0.5 = 1 + t2
T = t2 + 1.5
10T = 10t2 + 15 ---> (2)

by subtracting (2) - (1),
3T = 15, T = 5

so D = 35(T+1) = 35*6 = 210
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Re: Ron drives from his home to the airport to catch a flight.   [#permalink] 08 Mar 2019, 09:30
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