Bunuel wrote:
A cyclist traveled for two days. On the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling, what was her average speed on the second day?
A. 5 mph
B. 10 mph
C. 20 mph
D. 30 mph
E. 40 mph
Another approach: You can also solve this one with another sort of logic and number sense. Focus first on the time. Namely, 12 hours across 2 days can be broken down readily enough to 6 hours per day
on average. Since we know there was a 4-hour difference between days one and two, we can take the 4 and divide it by 2 and skew our 6-hour split by going 2 hours in either direction:
6 - 2 hours = 4 hours (Day 1)
6 + 2 hours = 8 hours (Day 2)
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12 hours altogether over two days, with the correct split
If the question asks about the
second day, pick a number in the middle, say, (B), 10 mph:
10 mph * 8 hours = 80 miles (Day 2)
20 mph * 4 hours = 80 miles (Day 1)
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12 hours altogether over two days, but only 160 total miles traveled--
TOO LOW. Out with (A) and (B), onto (D). Why (D)? Because regardless of whether it ends up being the answer, we will know definitively whether it is too high or too low.
30 mph * 8 hours = 240 miles (Day 2)
40 mph * 4 hours = 160 miles (Day 1)
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12 hours altogether over two days, but with 400 miles traveled--
TOO HIGH. Thus, (D) and (E) are out, and
(C), 20 mph, must be the answer.
This mental math is simple enough and takes about a minute to work through, maybe a minute and a half in a Day 2-type situation.
Cheers,
Andrew