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16 Dec 2025, 01:04
Kudos
Bookmarks
At 10:00 p.m., a cyclist is 10 miles from home on a straight road. From that time on, the cyclist continues riding farther from home at a constant speed of 3 minutes per mile, then turns around and rides back toward home at the same speed along the same road. If the cyclist must arrive back home at 10:48 p.m., how many additional miles can the cyclist travel away from home after 10:00 p.m. before turning around?
A. 2
B. 3
C. 6
D. 9
E. 12
at 10 PM cyclist is 10 miles away
distance covered extra be x miles at speed of 3 minutes per mile
net time of ride is 48 mins
total distance covered by cyclist is
(10+x) return and x is additional
3*(10+2x ) ; 30 + 6x
30+6x = 48
x = 3
option B
A. 2
B. 3
C. 6
D. 9
E. 12
at 10 PM cyclist is 10 miles away
distance covered extra be x miles at speed of 3 minutes per mile
net time of ride is 48 mins
total distance covered by cyclist is
(10+x) return and x is additional
3*(10+2x ) ; 30 + 6x
30+6x = 48
x = 3
option B
16 Dec 2025, 01:08
Kudos
Bookmarks
Bunuel
As a cyclist travels extra X miles, he or she will spend 3X minutes (as a cyclist spends 3 minutes for every mile ridden). After cyclist rode X (extra) miles and turns back he covers those X miles one more time, overall cyclist will spend 2*3X = 6X minutes on extra traveling and as he or she was 10 miles away from home 3*10 minutes is added. Overall, he or she needs to spend 48 minutes.
6X+30= 48
6X=18
X=3 miles
So, if he travels an extra 3 miles while being 10 miles away from home, he or she will be at home at 10:48 p.m.
16 Dec 2025, 01:11
Kudos
Bookmarks
First step is to account for the time lost to cover the 10 miles back home. Considering it's 3 mins/mile, that's 30 mins required in that segment of the trip. Since the cyclist needs to get home by 10.48pm, he needs to return to the start of the 10 mile stretch by (10.48 - 30 mins)
10.18pm.
The current time is 10 pm. Considering he can travel at 3 mins/mile, and the fact that he needs to get back to the current market by 10.18pm, he can travel a further (18/3) 6 miles. Since he will need to go and come back by then, we will need to divide this 6 miles by 2. Therefore, he can travel and additional 3 miles before turning back.
10.18pm.
The current time is 10 pm. Considering he can travel at 3 mins/mile, and the fact that he needs to get back to the current market by 10.18pm, he can travel a further (18/3) 6 miles. Since he will need to go and come back by then, we will need to divide this 6 miles by 2. Therefore, he can travel and additional 3 miles before turning back.
Bunuel
