Problem Solving

Ken and Lee left the same wayside gas station at 4:00 a.m., with Ken driving due east and Lee driving due south, both at the same constant speed. At 7:00 a.m. the same day, Ken halved his speed to make a turn, and turned 90° to his left and Lee, without changing his speed, turned 90° to his right. They both continued in straight lines at their speeds, and at 9:00 a.m. the same day, they were approximately 380 miles apart, as the crow flies. The speed at which Ken made his left turn is closest to which of the following integers?
A. 23
B. 29
C. 35
D. 41
E. 47




[spoiler]Made Up with the help of Matt@VeritasPrep![/spoiler]

Ignore this problem. Very poorly written.

The wording still isn't idiomatic ("took left" isn't American English, and "took turns" doesn't mean what you think it does) and the speeds are ambiguous. (Does "same speed" the second time mean that Lee also cut his speed in half, or that he continued at his original speed?) I think you want something more like

"Ken and Lee left the same wayside gas station at 4:00, with Ken driving due east and Lee driving due south, both at the same constant speed. At 7:00, each man halved his speed to make a turn, with Ken turning 90° to his left and Lee turning 90° to his right. They both continued in straight lines at this reduced speed, and at 9:00 were approximately 380 miles apart, as the crow flies. The speed at which Ken made his left turn is closest to which of the following integers?"

Matt@VeritasPrep wrote:The wording still isn't idiomatic ("took left" isn't American English, and "took turns" doesn't mean what you think it does) and the speeds are ambiguous. (Does "same speed" the second time mean that Lee also cut his speed in half, or that he continued at his original speed?) I think you want something more like

"Ken and Lee left the same wayside gas station at 4:00, with Ken driving due east and Lee driving due south, both at the same constant speed. At 7:00, each man halved his speed to make a turn, with Ken turning 90° to his left and Lee turning 90° to his right. They both continued in straight lines at this reduced speed, and at 9:00 were approximately 380 miles apart, as the crow flies. The speed at which Ken made his left turn is closest to which of the following integers?"

Thanks for the nice suggestion Matt, but I don't mean that Lee also halved his speed; I meant Lee continued with his original speed and only Ken halved his speed. Suggestions solicited. Moreover, doesn't the clock time suggested by you need A.M. or P.M.? How can we definitely conclude that they drove for exactly 5 hours from the wordings suggested by you? Just curious, although I regret for not being an American native.

OK, got it!

I think an American would assume that 4:00 and 7:00 belong to the same half of the day (either both AM or both PM) unless otherwise specified. (For instance, "I left at 4:00 and got in at 7:00" implies a three hour trip, but "I left at 4:00 AM and didn't get back until 7:00 at night!" indicates a fifteen hour trip.)

Our clock system is bad as our other systems of measurement, though - I much prefer the 24 hour clock!