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11 May 2026, 01:13
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (03:08) correct
28%
(03:02)
wrong
based on 87
sessions
History
Date
Time
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Not Attempted Yet
Damaso and Ernesto ran a 12-kilometer race at constant speeds. Damaso finished the race in 48 minutes, and Ernesto finished in 60 minutes. When Ernesto had twice as many kilometers left to run as Damaso, how many kilometers had they run in total?
A. 14 km
B. 15 km
C. 16 km
D. 17 km
E. 18 km
A. 14 km
B. 15 km
C. 16 km
D. 17 km
E. 18 km
11 May 2026, 07:10
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Speeds:
Damaso: 12 km in 48 min = 1/4 km/min
Ernesto: 12 km in 60 min = 1/5 km/min
Let t = minutes elapsed.
Distances run:
Damaso = t/4
Ernesto = t/5
Distances left:
Damaso = 12 − t/4
Ernesto = 12 − t/5
Given:
Ernesto had twice as many km left as Damaso:
12 − t/5 = 2(12 − t/4)
12 − t/5 = 24 − t/2
Multiply by 10:
120 − 2t = 240 − 5t
3t = 120
t = 40
Distances run then:
Damaso: 40/4 = 10 km
Ernesto: 40/5 = 8 km
Total = 18 km
Answer: E. 18 km
Damaso: 12 km in 48 min = 1/4 km/min
Ernesto: 12 km in 60 min = 1/5 km/min
Let t = minutes elapsed.
Distances run:
Damaso = t/4
Ernesto = t/5
Distances left:
Damaso = 12 − t/4
Ernesto = 12 − t/5
Given:
Ernesto had twice as many km left as Damaso:
12 − t/5 = 2(12 − t/4)
12 − t/5 = 24 − t/2
Multiply by 10:
120 − 2t = 240 − 5t
3t = 120
t = 40
Distances run then:
Damaso: 40/4 = 10 km
Ernesto: 40/5 = 8 km
Total = 18 km
Answer: E. 18 km
11 May 2026, 12:36
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Ernesto is E and Damaso is D.
Ratio of their times is 48mins : 60 mins = 4:5 respectively
That means ratio of their speeds is 5:4 respectively.
Now to find out the distance required:
12-E= 2(12-D)
The speeds are constant for both, so according to our speeds ratio 5:4, it means for every 5km D covers, E covers 4km. So now we just need to find the multiplicant for 5 and 4 such that the distance by E is twice D's distance:
12 - 5x = 2(12-4x) - Solve for x
x = 2
that means E has ran 5(2)km and D has ran 4(2)km, which simplify to 10 and 8 respectively
10km + 8 km = 18km
Ratio of their times is 48mins : 60 mins = 4:5 respectively
That means ratio of their speeds is 5:4 respectively.
Now to find out the distance required:
12-E= 2(12-D)
The speeds are constant for both, so according to our speeds ratio 5:4, it means for every 5km D covers, E covers 4km. So now we just need to find the multiplicant for 5 and 4 such that the distance by E is twice D's distance:
12 - 5x = 2(12-4x) - Solve for x
x = 2
that means E has ran 5(2)km and D has ran 4(2)km, which simplify to 10 and 8 respectively
10km + 8 km = 18km
