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15 Dec 2025, 09:54
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To return back to home cyclist needs 30 min considering 3 min/mile speed
3 min / mile x 10 mile = 30 min
he has spend addition 18 min (48-30 = 18).
in 18 min cyclist can cover : 18 min / 3 min/mile = 6 miles
hence he can go further 3 mile away from the point and 3 mile return to the point.
hence 3 is the answer
3 min / mile x 10 mile = 30 min
he has spend addition 18 min (48-30 = 18).
in 18 min cyclist can cover : 18 min / 3 min/mile = 6 miles
hence he can go further 3 mile away from the point and 3 mile return to the point.
hence 3 is the answer
msignatius
15 Dec 2025, 09:55
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A question that can be quite easily solved with more logic and less math - and like word problems in general, with careful reading 
Okay, so, we're at 10pm and the cyclist is 10 miles from home. His pace - 3 minutes a mile, or 20 miles per hour. That means, if he were to go back the 10 miles now, he'd reach by 10.30pm. What's his curfew though? 10.48pm. So, he'll be home with 18 minutes to spare. But the cyclist wishes to maximize his cycling time (who wouldn't if they can comfortably manage that pace?
). But anyway, every minute he cycles away from home, he will have to add another minute to cycle back. That gives him an extra 9 minutes to cycle forth. That's another 3 miles at 3 minutes a mile. Answer - B.
Okay, so, we're at 10pm and the cyclist is 10 miles from home. His pace - 3 minutes a mile, or 20 miles per hour. That means, if he were to go back the 10 miles now, he'd reach by 10.30pm. What's his curfew though? 10.48pm. So, he'll be home with 18 minutes to spare. But the cyclist wishes to maximize his cycling time (who wouldn't if they can comfortably manage that pace?
). But anyway, every minute he cycles away from home, he will have to add another minute to cycle back. That gives him an extra 9 minutes to cycle forth. That's another 3 miles at 3 minutes a mile. Answer - B.Bunuel
15 Dec 2025, 09:56
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Consider this diagram,
Home_________X______________B
The distance between home and point X at 10 AM is 10 miles (given). Let's assume the distance between point X and B (additional miles traveled away from home before turning around) to be M miles. The cyclist arrives back home at 10:48, i.e., 48 mins were taken to cover a distance of 2M+10 miles.
Speed is 3 mins/miles, which is 1/3 miles/mins
So basically now you have,
2M+10 miles = 48*(1/3)
2M = 6
M = 3 (Option B)
Home_________X______________B
The distance between home and point X at 10 AM is 10 miles (given). Let's assume the distance between point X and B (additional miles traveled away from home before turning around) to be M miles. The cyclist arrives back home at 10:48, i.e., 48 mins were taken to cover a distance of 2M+10 miles.
Speed is 3 mins/miles, which is 1/3 miles/mins
So basically now you have,
2M+10 miles = 48*(1/3)
2M = 6
M = 3 (Option B)
