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.
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 ?
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
