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09 Apr 2026, 17:06
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B
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Difficulty:
85%
(hard)
Question Stats:
60% (03:11) correct
40%
(02:59)
wrong
based on 85
sessions
History
Date
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Not Attempted Yet
Gero cycled 12 miles in the first 40 minutes of his journey, but realized that he would be 5 minutes late if he continued at this speed. He increased his speed by one-half for the remainder of the trip and arrived 10 minutes early. How many miles was Gero’s journey?
(A) 24
(B) 25.5
(C) 27
(D) 30
(E) 33
(A) 24
(B) 25.5
(C) 27
(D) 30
(E) 33
Updated on: 10 Apr 2026, 04:53
Originally posted by MartyMurray on 09 Apr 2026, 20:00.
Last edited by MartyMurray on 10 Apr 2026, 04:53, edited 1 time in total.
Last edited by MartyMurray on 10 Apr 2026, 04:53, edited 1 time in total.
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Gero cycled 12 miles in the first 40 minutes of his journey, but realized that he would be 5 minutes late if he continued at this speed. He increased his speed by one-half for the remainder of the trip and arrived 10 minutes early. How many miles was Gero’s journey?
Gero cycled 12 miles in the first 40 minutes of his journey
Gero's speed for first 40 minutes: 12/(40/60) = 12/(2/3) = 18
He increased his speed by one-half for the remainder of the trip
Gero's speed for remainder of the trip: 18 × 1.5 = 27
Gero ... realized that he would be 5 minutes late if he continued at this speed. He increased his speed ... and arrived 10 minutes early.
Difference between time for entire trip at 18 mph and actual time: 5 - (-10) = 15 minutes = 1/4 hour
Distance: D
Distance at 18 mph: 12
Distance at faster speed: D - 12
D/18 - (40/60 + (D - 12)/27) = 1/4
1.5D/27 - 18/27 - (D - 12)/27 = 1/4
1.5D - 18 - D + 12 = 27/4
0.5D - 6 = 27/4
2D - 24 = 27
D = 25.5
(A) 24
(B) 25.5
(C) 27
(D) 30
(E) 33
Correct answer: B
Gero cycled 12 miles in the first 40 minutes of his journey
Gero's speed for first 40 minutes: 12/(40/60) = 12/(2/3) = 18
He increased his speed by one-half for the remainder of the trip
Gero's speed for remainder of the trip: 18 × 1.5 = 27
Gero ... realized that he would be 5 minutes late if he continued at this speed. He increased his speed ... and arrived 10 minutes early.
Difference between time for entire trip at 18 mph and actual time: 5 - (-10) = 15 minutes = 1/4 hour
Distance: D
Distance at 18 mph: 12
Distance at faster speed: D - 12
D/18 - (40/60 + (D - 12)/27) = 1/4
1.5D/27 - 18/27 - (D - 12)/27 = 1/4
1.5D - 18 - D + 12 = 27/4
0.5D - 6 = 27/4
2D - 24 = 27
D = 25.5
(A) 24
(B) 25.5
(C) 27
(D) 30
(E) 33
Correct answer: B
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09 Apr 2026, 20:05
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Initial speed = 12/40 = 0.3 miles per minute
New speed = 0.3 × 1.5 = 0.45 miles per minute
Let total distance = D miles
Let scheduled time = T minutes
If he continued at original speed:
D / 0.3 = T + 5
Actual journey:
40 + (D − 12)/0.45 = T − 10
From first equation:
T = D/0.3 − 5
Substitute:
40 + (D − 12)/0.45 = D/0.3 − 15
Convert:
D/0.3 = 10D/3
(D − 12)/0.45 = 20(D − 12)/9
So:
40 + 20(D − 12)/9 = 10D/3 − 15
Multiply by 9:
360 + 20(D − 12) = 30D − 135
360 + 20D − 240 = 30D − 135
120 + 20D = 30D − 135
255 = 10D
D = 25.5
Answer: 25.5
Option: B
New speed = 0.3 × 1.5 = 0.45 miles per minute
Let total distance = D miles
Let scheduled time = T minutes
If he continued at original speed:
D / 0.3 = T + 5
Actual journey:
40 + (D − 12)/0.45 = T − 10
From first equation:
T = D/0.3 − 5
Substitute:
40 + (D − 12)/0.45 = D/0.3 − 15
Convert:
D/0.3 = 10D/3
(D − 12)/0.45 = 20(D − 12)/9
So:
40 + 20(D − 12)/9 = 10D/3 − 15
Multiply by 9:
360 + 20(D − 12) = 30D − 135
360 + 20D − 240 = 30D − 135
120 + 20D = 30D − 135
255 = 10D
D = 25.5
Answer: 25.5
Option: B
