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Difficulty:
55%
(hard)
Question Stats:
68% (03:02) correct
32%
(03:12)
wrong
based on 34
sessions
History
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Minho, Jisoo, and Taeyang are assigned the task of adjusting insurance policy premiums. Minho would take 1 hour longer than Jisoo to complete the task but one-third as long as Taeyang . If they worked in pairs, Minho and Taeyang would take 75 percent longer than Taeyang and Jisoo.
If Minho, Jisoo, and Taeyang worked together, how long would it take them to complete the task ?
A. 30 minutes
B. 36 minutes
C. 45 minutes
D. 72 minutes
E. 120 minutes
If Minho, Jisoo, and Taeyang worked together, how long would it take them to complete the task ?
A. 30 minutes
B. 36 minutes
C. 45 minutes
D. 72 minutes
E. 120 minutes
10 Mar 2026, 01:55
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Great Work and Rate problem — this one tests a concept I call "decoding relative time statements before setting up equations."
Key concept: Work Rate problems with relative time comparisons (Problem Solving).
Step 1 — Assign variables based on given relationships.
Let Jisoo's time = J hours.
- Minho takes 1 hour longer than Jisoo → M = J + 1
- Minho takes one-third as long as Taeyang → M = T/3, so T = 3M = 3(J + 1)
Step 2 — Set up the combined pair times.
When two people work together, combined time = (A × B)/(A + B).
- Minho + Taeyang time = (J+1) × 3(J+1) / ((J+1) + 3(J+1)) = 3(J+1)2/4(J+1) = 3(J+1)/4
- Taeyang + Jisoo time = 3(J+1) × J / (3(J+1) + J) = 3J(J+1)/(4J+3)
Step 3 — Apply the "75% longer" condition.
"75% longer" means M+T pair time = 1.75 × T+J pair time:
3(J+1)/4 = 1.75 × 3J(J+1)/(4J+3)
Divide both sides by (J+1) [valid since J > 0]:
3/4 = 5.25J/(4J+3)
3(4J+3) = 21J
12J + 9 = 21J
J = 1 hour
Step 4 — Find individual times.
Jisoo = 1 hour (60 min), Minho = 2 hours (120 min), Taeyang = 3 × 2 = 6 hours (360 min)
Step 5 — Calculate combined rate for all three.
Combined rate = 1/1 + 1/2 + 1/6 = 6/6 + 3/6 + 1/6 = 10/6 per hour
Combined time = 6/10 hours = 0.6 hours = 36 minutes
Answer: B (36 minutes)
Common trap: Students read "Minho takes one-third as long as Taeyang" and write T = 3J (mistakenly linking to Jisoo rather than Minho). Always track exactly who each comparison refers to. Here, both comparisons are about Minho: 1 hour longer than Jisoo, one-third as long as Taeyang.
Takeaway: In multi-person rate problems, express every individual time in terms of one variable first — then build combined-pair equations. Trying to work with multiple variables simultaneously is where most errors sneak in.
Key concept: Work Rate problems with relative time comparisons (Problem Solving).
Step 1 — Assign variables based on given relationships.
Let Jisoo's time = J hours.
- Minho takes 1 hour longer than Jisoo → M = J + 1
- Minho takes one-third as long as Taeyang → M = T/3, so T = 3M = 3(J + 1)
Step 2 — Set up the combined pair times.
When two people work together, combined time = (A × B)/(A + B).
- Minho + Taeyang time = (J+1) × 3(J+1) / ((J+1) + 3(J+1)) = 3(J+1)2/4(J+1) = 3(J+1)/4
- Taeyang + Jisoo time = 3(J+1) × J / (3(J+1) + J) = 3J(J+1)/(4J+3)
Step 3 — Apply the "75% longer" condition.
"75% longer" means M+T pair time = 1.75 × T+J pair time:
3(J+1)/4 = 1.75 × 3J(J+1)/(4J+3)
Divide both sides by (J+1) [valid since J > 0]:
3/4 = 5.25J/(4J+3)
3(4J+3) = 21J
12J + 9 = 21J
J = 1 hour
Step 4 — Find individual times.
Jisoo = 1 hour (60 min), Minho = 2 hours (120 min), Taeyang = 3 × 2 = 6 hours (360 min)
Step 5 — Calculate combined rate for all three.
Combined rate = 1/1 + 1/2 + 1/6 = 6/6 + 3/6 + 1/6 = 10/6 per hour
Combined time = 6/10 hours = 0.6 hours = 36 minutes
Answer: B (36 minutes)
Common trap: Students read "Minho takes one-third as long as Taeyang" and write T = 3J (mistakenly linking to Jisoo rather than Minho). Always track exactly who each comparison refers to. Here, both comparisons are about Minho: 1 hour longer than Jisoo, one-third as long as Taeyang.
Takeaway: In multi-person rate problems, express every individual time in terms of one variable first — then build combined-pair equations. Trying to work with multiple variables simultaneously is where most errors sneak in.
