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24 Mar 2021, 03:00
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
65% (03:25) correct
35%
(03:28)
wrong
based on 131
sessions
History
Date
Time
Result
Not Attempted Yet
Santa traveled to one home at x miles per hour. Realizing he was running late, he then doubled his speed to the next home 20 miles away. If Santa traveled a total of 36 miles at an average speed of 240 miles per hour, approximately how long did it take him, in minutes, to travel to the first home?
A. 5.5
B. 6.0
C. 6.5
D. 7.0
E. 7.5
A. 5.5
B. 6.0
C. 6.5
D. 7.0
E. 7.5
24 Mar 2021, 23:50
Kudos
Bookmarks
Total distance travelled by Santa = 36 miles. Average speed of Santa = 240 miles per hour.
=> Total time taken by Santa = \(\frac{36}{240}\) hour.
Distance between first home and second home = 20 miles.
=> Distance between starting point of Santa and first home = 36 - 20 = 16 miles.
Speed to first home = x miles per hour, speed to second home = 2x miles per hour.
Time required to travel to the first home = \(\frac{16}{x}\) hour = \(\frac{16}{x}\) * 60 minutes =?
Total time taken by Santa = Time to travel to first home + time to travel to second home
=> \(\frac{36}{240}\)= \(\frac{16}{x}\) + \(\frac{20}{2x}\) = \(\frac{16 + 10}{x}\) = \(\frac{26}{x}\)
=> x = \(\frac{240 * 26}{36}\) = \(\frac{520}{3}\) miles per hour
Time required to travel to the first home = \(\frac{16}{x}\) hour = \(\frac{16}{(520/3)}\) hour = \(\frac{16 * 3}{520}\) * 60 minutes \(\approx\) 5.5 minutes.
So, correct answer is option A.
=> Total time taken by Santa = \(\frac{36}{240}\) hour.
Distance between first home and second home = 20 miles.
=> Distance between starting point of Santa and first home = 36 - 20 = 16 miles.
Speed to first home = x miles per hour, speed to second home = 2x miles per hour.
Time required to travel to the first home = \(\frac{16}{x}\) hour = \(\frac{16}{x}\) * 60 minutes =?
Total time taken by Santa = Time to travel to first home + time to travel to second home
=> \(\frac{36}{240}\)= \(\frac{16}{x}\) + \(\frac{20}{2x}\) = \(\frac{16 + 10}{x}\) = \(\frac{26}{x}\)
=> x = \(\frac{240 * 26}{36}\) = \(\frac{520}{3}\) miles per hour
Time required to travel to the first home = \(\frac{16}{x}\) hour = \(\frac{16}{(520/3)}\) hour = \(\frac{16 * 3}{520}\) * 60 minutes \(\approx\) 5.5 minutes.
So, correct answer is option A.
03 Apr 2021, 10:46
Kudos
Bookmarks
Bunuel
Solution:
We see that the distance to the first home is 36 - 20 = 16 miles. We can create the equation:
16/x + 20/(2x) = 36/240
16/x + 10/x = 3/20
26/x = 3/20
3x = 520
x = 520/3
Since Santa’s speed is 520/3 mph to the first home, the time needed is 16/(520/3) = 48/520 = 12/130 of an hour or 12/130 x 60 ≈ 5.5 minutes.
Answer: A
