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# Suzy estimated both the distance of her trip to her hometown, in miles

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Math Expert
Joined: 02 Sep 2009
Posts: 53831
Suzy estimated both the distance of her trip to her hometown, in miles  [#permalink]

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22 Oct 2018, 00:14
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Difficulty:

45% (medium)

Question Stats:

60% (01:36) correct 40% (01:35) wrong based on 74 sessions

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Suzy estimated both the distance of her trip to her hometown, in miles, and the average speed, in miles per hour. Was the estimated time within 30 minutes of the actual time of the trip?

(1) Suzy’s estimate for the distance was within 10 miles of the actual distance.
(2) Suzy’s estimate for her average speed was within 5 miles per hour of her actual average speed.

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Math Expert
Joined: 02 Aug 2009
Posts: 7445
Re: Suzy estimated both the distance of her trip to her hometown, in miles  [#permalink]

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22 Oct 2018, 19:42
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1
Suzy estimated both the distance of her trip to her hometown, in miles, and the average speed, in miles per hour. Was the estimated time within 30 minutes of the actual time of the trip?

(1) Suzy’s estimate for the distance was within 10 miles of the actual distance.
(2) Suzy’s estimate for her average speed was within 5 miles per hour of her actual average speed.

Let us take combined because clearly the statement individually are insufficient..

Now many of us can mistake for C as we have estimate of speed and distance. But we do not know actuals, and can have effect as shown below

Two cases..
Speed actual 60mph .. her estimate 55-65mph
I...Distance actual 120 miles...her estimate 110-130
Actual time 120/60=2 hrs... Her estimate varies from 130/55=2 hr 22 min to 110/65= 1 hr 42 min...
So within 30 minutes..
II. Let the distance now be 1200 miles... Her estimate 1190 to 1210
Distance is 10 fold and speed is same so the range also will be nearly 10 times..
Actual 1200÷60=20 hr
Range due to estimate 1210÷55=22hr to 1190÷65=~18
So there is a difference of 2 hrs on either side so > 30 min of actuals

E
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Re: Suzy estimated both the distance of her trip to her hometown, in miles   [#permalink] 22 Oct 2018, 19:42
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