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Difficulty:
45%
(medium)
Question Stats:
74% (02:52) correct
26%
(02:56)
wrong
based on 141
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Ashphalt paver A can pave a road in 3 hours, and asphalt paver B can pave the same road in 2 hours 24 minutes. If both pavers work together at their constant rates but stop working 15 minutes before the road is completely paved, what fraction of the road remains unpaved?
A) 1/8
B) 3/16
C) 1/5
D) 1/4
E) 1/3
A) 1/8
B) 3/16
C) 1/5
D) 1/4
E) 1/3
12 Mar 2026, 06:21
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kevincan
A does the work in 3 hrs.
B does the work in 2 hrs 24 minutes = 2 * (24/60) = (12/5) hrs
Work = 12 units
A 3 hrs , efficiency = 4 units
B (12/5) hrs , efficiency = 5 units.
A and B working together, for 1 hour completes (4+5) = 9 units.
To complete 3 units, we need 20 minutes.
So, total time = 1 hr 20 minutes.
But, we stop the work in 15 minutes before completion.
100% work is completed in 1 hr 20 minutes = 80 minutes.
15 minutes of 80 minutes is left undone.
Fraction left = (15/80) = 3/16 .
OR
% of work completed in 1 hr 05 minutes = 65 minutes.
% of work completed in 65 minutes = (100*65)/80 = 81.25% work is completed.
Work remaining = 100 - 81.25 = 18.75
Fraction of work left = (18.75/100) = 3/16
Option B
13 Mar 2026, 09:50
Kudos
Bookmarks
Let me walk through this step by step.
Step 1: Find each machine's rate.
Machine A paves the road in 3 hours, so its rate = 1/3 of the road per hour.
Machine B paves the road in 2 hours 24 minutes = 12/5 hours, so its rate = 5/12 of the road per hour.
Step 2: Find their combined rate.
Combined rate = 1/3 + 5/12 = 4/12 + 5/12 = 9/12 = 3/4 of the road per hour.
Step 3: Find how long it would take them to finish together.
Time to finish = 1 ÷ 3/4 = 4/3 hours = 1 hour 20 minutes = 80 minutes.
Step 4: They stop 15 minutes before the road is completely paved.
This means they only work for 80 - 15 = 65 minutes, which is 65/60 = 13/12 hours.
Step 5: Find how much they paved.
Work = Rate × Time = 3/4 × 13/12 = 39/48 = 13/16 of the road.
Step 6: Find the unpaved fraction.
Unpaved = 1 - 13/16 = 3/16.
Answer: B
Key principle: In work-rate problems, always convert everything to the same units first (hours or minutes — pick one). Then remember: Work = Rate × Time. The fraction remaining is just 1 minus the fraction completed.
Step 1: Find each machine's rate.
Machine A paves the road in 3 hours, so its rate = 1/3 of the road per hour.
Machine B paves the road in 2 hours 24 minutes = 12/5 hours, so its rate = 5/12 of the road per hour.
Step 2: Find their combined rate.
Combined rate = 1/3 + 5/12 = 4/12 + 5/12 = 9/12 = 3/4 of the road per hour.
Step 3: Find how long it would take them to finish together.
Time to finish = 1 ÷ 3/4 = 4/3 hours = 1 hour 20 minutes = 80 minutes.
Step 4: They stop 15 minutes before the road is completely paved.
This means they only work for 80 - 15 = 65 minutes, which is 65/60 = 13/12 hours.
Step 5: Find how much they paved.
Work = Rate × Time = 3/4 × 13/12 = 39/48 = 13/16 of the road.
Step 6: Find the unpaved fraction.
Unpaved = 1 - 13/16 = 3/16.
Answer: B
Key principle: In work-rate problems, always convert everything to the same units first (hours or minutes — pick one). Then remember: Work = Rate × Time. The fraction remaining is just 1 minus the fraction completed.
