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Parisa traveled from her home to the gym by the same route on two consecutive days. On the first day, she jogged 3/5 of the distance at 12 km/h and walked the remaining distance at 6 km/h. On the second day, she jogged at 12 km/h for 3/5 of the time and walked at 6 km/h for the remaining time. If the total time on the first day was 3 minutes longer than on the second day, what is the distance from her home to the gym?
A. 2 km
B. 4 km
C. 6 km
D. 8 km
E. 12 km
A. 2 km
B. 4 km
C. 6 km
D. 8 km
E. 12 km
05 Mar 2026, 22:56
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kevincan
Let’s assume the distance to be as d.
Case 1: (3/5) of the distance at 12 kmph.
Time t1 = ?
12 = (3/5)d /t1
t1 = d/20
(2/5) of the distance at 6 kmph.
t2 = (d/15)
Total time = (d/20)+(d/15) = (7d/60)
Case 2:
Let’s find the total distance d.
d = 12*(3/5)t + 6*(2/5)t
Solving, we get
t = 5d/48
The difference of times from case 1 is 3 minutes more than time from case 2.
(7d/60) - (5d/48) = (3/60)
Solving we get, d=4 km
Option B
07 Mar 2026, 07:00
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Key concept being tested: Distance-Speed-Time with mixed conditions — specifically the difference between dividing a distance into fractions vs. dividing time into fractions. This is one of the most common traps in GMAT speed questions.
The trap: Most students set up both days identically using distance fractions. Day 2 says she jogged "3/5 of the time" — not 3/5 of the distance. The moment you miss that word, both equations collapse into the same thing and you can't find a unique answer.
Step 1 — Set up Day 1 (fraction of distance).
Let d = total distance (km). She jogs 3d/5 at 12 km/h and walks 2d/5 at 6 km/h.
Time1 = (3d/5)/12 + (2d/5)/6 = d/20 + d/15
Finding common denominator: d/20 + d/15 = 3d/60 + 4d/60 = 7d/60
Step 2 — Set up Day 2 (fraction of time). This is where it changes.
Let total time on Day 2 = T. She jogs for 3T/5 at 12 km/h and walks for 2T/5 at 6 km/h.
Distance = 12 x (3T/5) + 6 x (2T/5) = 36T/5 + 12T/5 = 48T/5
Since this equals d: T = 5d/48
Step 3 — Use the 3-minute difference.
Day 1 took 3 minutes longer than Day 2. Convert 3 minutes to hours: 3/60 = 1/20.
7d/60 - 5d/48 = 1/20
Find common denominator (240):
(28d - 25d)/240 = 1/20
3d/240 = 1/20
d = 240/(20 x 3) = 4 km
Answer: B
Takeaway: Any time a problem switches between "fraction of distance" and "fraction of time" across two scenarios, write those words explicitly before setting up your equation — that single swap changes the entire structure of the algebra.
— Kavya | 725 (99th percentile), GMAT Focus Edition
The trap: Most students set up both days identically using distance fractions. Day 2 says she jogged "3/5 of the time" — not 3/5 of the distance. The moment you miss that word, both equations collapse into the same thing and you can't find a unique answer.
Step 1 — Set up Day 1 (fraction of distance).
Let d = total distance (km). She jogs 3d/5 at 12 km/h and walks 2d/5 at 6 km/h.
Time1 = (3d/5)/12 + (2d/5)/6 = d/20 + d/15
Finding common denominator: d/20 + d/15 = 3d/60 + 4d/60 = 7d/60
Step 2 — Set up Day 2 (fraction of time). This is where it changes.
Let total time on Day 2 = T. She jogs for 3T/5 at 12 km/h and walks for 2T/5 at 6 km/h.
Distance = 12 x (3T/5) + 6 x (2T/5) = 36T/5 + 12T/5 = 48T/5
Since this equals d: T = 5d/48
Step 3 — Use the 3-minute difference.
Day 1 took 3 minutes longer than Day 2. Convert 3 minutes to hours: 3/60 = 1/20.
7d/60 - 5d/48 = 1/20
Find common denominator (240):
(28d - 25d)/240 = 1/20
3d/240 = 1/20
d = 240/(20 x 3) = 4 km
Answer: B
Takeaway: Any time a problem switches between "fraction of distance" and "fraction of time" across two scenarios, write those words explicitly before setting up your equation — that single swap changes the entire structure of the algebra.
— Kavya | 725 (99th percentile), GMAT Focus Edition
