## In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour

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### In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour

by BTGmoderatorDC » Mon Jan 24, 2022 6:29 pm

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In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?

(1) Joan’s estimate for the distance was within 5 miles of the actual distance.

(2) Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.

OA E

Source: Official Guide

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### Re: In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per

by [email protected] » Tue Jan 25, 2022 6:33 am

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## Global Stats

BTGmoderatorDC wrote:
Mon Jan 24, 2022 6:29 pm
In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?

(1) Joan’s estimate for the distance was within 5 miles of the actual distance.

(2) Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.

OA E

Source: Official Guide
Target question: Was Joan's ESTIMATE within 0.5 hour of the ACTUAL TIME that the trip took?

Statement 1: Joan’s ESTIMATE for the distance was within 5 miles of the ACTUAL distance.
Travel time = distance/speed

Statement 1 provides information regarding the accuracy of Joan's estimation of the travel distance, BUT it does not provide any information regarding her accuracy in estimating her speed.
As such, statement 1 is NOT SUFFICIENT

Statement 2: Joan’s estimate for her average speed was within 10 miles per hour of her actual average speed.
Statement 2 provides information regarding the accuracy of Joan's estimation of her average speed, BUT it does not provide any information regarding her accuracy in estimating the travel distance.
As such, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Let's test some numbers.
There are several possible scenarios that satisfy BOTH statements. Here are two:
Case a: Joan's estimates were PERFECTLY accurate. In this case, her ACTUAL travel time was definitely WITHIN 0.5 hours of her ESTIMATED travel.

Case b: Joan's ESTIMATED distance and average speed were 8 miles and 8 miles per hour respectively, and the ACTUAL distance and average speed were 5 miles and 1 mile per hour respectively. So, Joan's ESTIMATED travel time = 8/8 = 1 hour, and her ACTUAL travel time = 5/1 = 5 hours. In this case, Joan's ACTUAL travel time was NOT WITHIN 0.5 hours of her ESTIMATED travel.

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT