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Joe always runs around the track at a rate of 30 laps per 75 minutes,

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Joe always runs around the track at a rate of 30 laps per 75 minutes, [#permalink] New post   26 Dec 2023, 00:48
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64% (01:58) correct 35% (02:15) wrong based on 14 sessions

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Joe always runs around the track at a rate of 30 laps per 75 minutes, and Carl always runs around the track at a rate of 20 laps per 40 minutes. They start running at the same time.


Quantity A
Quantity B
Time taken, in minutes, for Joeand Carl to run a combined distance of 99 laps
222.75 minutes




A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.



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Re: Joe always runs around the track at a rate of 30 laps per 75 minutes, [#permalink] New post   06 Jan 2024, 23:03
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joe 30 laps in 75 min
carl 20 lap in 40 mins

joe 20 laps in = 75/30 * 20 = 50 min
therefore 40 laps of joe = 100 mins , 40 laps of carl = 80 mins
19 laps remaining, 10 laps of carl = 20 mins, 9 laps of joe = 22. 5 mins
joe total time for 49 laps =100+22.5 = 122.5 mins
carl total time for 50 laps = 80 + 20 = 100 mins
122.5 + 100 = 222.5 mins
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Re: Joe always runs around the track at a rate of 30 laps per 75 minutes, [#permalink] New post   09 Jan 2024, 20:26
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Distance = Rate x Time, or Rate = Distance/Time

Joe's rate = 30 laps / 75 min = 0.4 laps / min
Carl's rate = 20 laps / 40 min = 0.5 laps / min

Since they start at the same time and it's asking for a combined distance of 99 laps, plug the rates back in:
(Joe's rate + Carl's rate) * time = 99 laps
(0.4 + 0.5) laps/min * time = 99 laps
time = 110 min
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Re: Joe always runs around the track at a rate of 30 laps per 75 minutes, [#permalink]
09 Jan 2024, 20:26
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