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Difficulty:
85%
(hard)
Question Stats:
38% (03:13) correct
62%
(02:45)
wrong
based on 26
sessions
History
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Paraskevas travels 20 kilometers at a constant speed and returns along the same route at a speed that is 2 km/h higher. His return trip takes 6 minutes less than the initial trip. Which of the following is closest to the speed in km/h of his return trip?
A. 15
B. 18
C. 20
D. 21
E. 22
A. 15
B. 18
C. 20
D. 21
E. 22
26 Mar 2026, 02:10
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This is a Distance and Speed problem, and the trap is the units. Most people set up the algebra and get confused because 6 minutes doesn't fit neatly into a km/h equation until you convert.
1. Let initial speed = v km/h. Return speed = v + 2 km/h.
2. Time for initial trip = 20/v hours. Time for return = 20/(v+2) hours.
3. Return trip is 6 minutes faster. Convert to hours: 6 min = 1/10 hr.
Set up: 20/v - 20/(v+2) = 1/10
4. Multiply through by 10v(v+2):
200(v+2) - 200v = v(v+2)
400 = v^2 + 2v
5. This doesn't factor cleanly to an integer. So I'd back-solve from the answer choices instead. The question asks for the RETURN speed, so let me test:
Return = 22 (initial = 20): 20/20 - 20/22 = 1/11 hr = about 5.45 min. Too low.
Return = 21 (initial = 19): 20/19 - 20/21 = 40/399 hr = about 6.01 min. Close enough.
6. Answer: C (21 km/h)
The quadratic gives v approximately 19, so return speed is approximately 21. Back-solving confirms it. On rate/time problems like this, if the algebra goes messy, just plug the answer choices in directly. Way faster than forcing a quadratic you can't factor.
1. Let initial speed = v km/h. Return speed = v + 2 km/h.
2. Time for initial trip = 20/v hours. Time for return = 20/(v+2) hours.
3. Return trip is 6 minutes faster. Convert to hours: 6 min = 1/10 hr.
Set up: 20/v - 20/(v+2) = 1/10
4. Multiply through by 10v(v+2):
200(v+2) - 200v = v(v+2)
400 = v^2 + 2v
5. This doesn't factor cleanly to an integer. So I'd back-solve from the answer choices instead. The question asks for the RETURN speed, so let me test:
Return = 22 (initial = 20): 20/20 - 20/22 = 1/11 hr = about 5.45 min. Too low.
Return = 21 (initial = 19): 20/19 - 20/21 = 40/399 hr = about 6.01 min. Close enough.
6. Answer: C (21 km/h)
The quadratic gives v approximately 19, so return speed is approximately 21. Back-solving confirms it. On rate/time problems like this, if the algebra goes messy, just plug the answer choices in directly. Way faster than forcing a quadratic you can't factor.
