2. 外语
  3. Khalil drove 120 kilometers in a certain amount of time. What was his average speed, in kilometers per hour, during this time? (

Khalil drove 120 kilometers in a certain amount of time. What was his average speed, in kilometers per hour, during this time? (

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问题 Khalil drove 120 kilometers in a certain amount of time. What was his average speed, in kilometers per hour, during this time?
(1) If Khalil had driven at an average speed that was 5 kilometers per hour faster, his driving time would have been reduced by 20 minutes.
(2) If Khalil had driven at an average speed that was 25% faster, his driving time would have been reduced by 20%.
选项 A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.
答案A
解析 Let r be Khalil’s average speed in kilometers per hour and let t be Khalil’s time in hours. Then
rt = 120, or t =120/r. What is the value of r ?
(1)    If Khalil’s speed had been (r + 5) kilometers per hour, then his driving time would have
been (t-1/3) hours.
(r + 5) ( t -1/3) = 120                   Statement (1)
                                 substitute t=120/r
(r + 5)(360-r)=360r                    multiply both sides by 3r
360r -r2 + 1,800 - 5r = 360r   expand left side subtract 360r
-(r + 45)(r - 40) = 0                    from both sides
-r2 + 1,800 - 5r = 0         factor the left side
Although there are two possible values for r, namely r = -45 and r = 40, only the positive value of r is consistent with the context. Therefore, r= 40; SUFFICIENT
(2)    If Khali’s speed had been 1.25r kilometers per hour, then his driving time would have been 0.8/ hours. It follows that (1.25r)(0.8t) = 120, or rt = 120, which provides no additional information to the given information; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
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