Bill rides his bile to work in the morning on a route that is 18 km long. Did Bill take longer than 40 minutes to get to work this morning? (1 km = approximately 0.6 miles)
1) Bill's average speed on the trip this morning was greater than 18 miles per hour.
2) Bill's average speed on the trip this morning was less than 20 miles per hour.
Please assist with above problem.
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Bill rides his bile to work in the morning on a route that i
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alanforde800Maximus
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Since the two statements are in terms of MILES PER HOUR, rephrase the question stem in terms of MILES PER HOUR.alanforde800Maximus wrote:Bill rides his bike to work in the morning on a route that is 18 km long. Did Bill take longer than 40 minutes to get to work this morning? (1 km = approximately 0.6 miles)
1) Bill's average speed on the trip this morning was greater than 18 miles per hour.
2) Bill's average speed on the trip this morning was less than 20 miles per hour.
Please assist with above problem.
40 minutes = 2/3 of an hour.
Determine the rate needed to travel 18 km in 2/3 of an hour:
(18 km)/(2/3 hour) * (0.6 miles)/(1 km) = (27)(0.6) = 16.2 miles per hour.
Note that the units in red CANCEL OUT, leaving the resulting value in terms of miles per hour.
If Bill travels at 16.2 miles per hour, he will take exactly 40 minutes to travel 18km.
Implication:
Bill will take LONGER THAN 40 MINUTES if his rate is LESS THAN 16.2 MILES PER HOUR.
Question stem, rephrased:
Was Bill's average speed less than 16.2 miles per hour?
Statement 1:
Here, Bill's average speed was definitely NOT less than 16.2 miles per hour.
SUFFICIENT.
Statement 2:
It's possible that Bill's average speed was 17 miles per hour, in which case it was NOT less than 16.2 miles per hour.
It's possible that Bill's average speed was 16 miles per hour, in which case it WAS less than 16.2 miles per hour.
INSUFFICIENT.
The correct answer is A.
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We are given that Bill rides his bike to work in the morning on a route that is 18 km long. We are asked if time > 40 minutes ?alanforde800Maximus wrote:Bill rides his bile to work in the morning on a route that is 18 km long. Did Bill take longer than 40 minutes to get to work this morning? (1 km = approximately 0.6 miles)
1) Bill's average speed on the trip this morning was greater than 18 miles per hour.
2) Bill's average speed on the trip this morning was less than 20 miles per hour.
While the question is asking about time, we see that our statements provide information about Bill's' rate, not his time. Thus, if we are able to manipulate the question to ask about rate (in miles per hour), we will be able to more easily determine the answer. So let's manipulate the question.
Is distance/rate > 40 minutes ?
Since we know that distance is 18 km, we can use that for the distance value in the question.
Is 18 km/rate > 40 minutes ?
Is rate < 18 km/40 mins ?
Since our statements express the rate in miles per hour, we want to convert minutes to hours and kilometers to miles.
Since 0.6 miles = 1 km, 18 km = 18 x 0.6 = 10.8 miles
Since 60 minutes = 1 hour, 40 minutes = 40/60 = 2/3 hour.
Thus, our new question is:
Is rate < 10.8 miles/(2/3 hour) ?
Is rate < 16.2 mph?
Statement One Alone:
Bill's average speed on the trip this morning was greater than 18 miles per hour.
Since Bill's average rate was greater than 18 mph, we know his rate WAS NOT less than 16.2 mph. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
Bill's average speed on the trip this morning was less than 20 miles per hour.
Although Bill's rate was less than 20 mph, we don't know whether it was actually less than 16.2 mph. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Answer: A
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