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Posted 3 months ago
Math Problem: A bus comes by Jerry's bus stop every 20 minutes starting at exactly 5:13 a.m. If Jerry shows up at exactly 8:358: 35 a.m., how many minutes will he have to wait for the next bus?
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Answer from Sia
Posted 3 months ago
Solution by Steps
step 1
Calculate the time from the first bus at 5:13 a.m. to Jerry's arrival at 8:35 a.m
step 2
Convert both times to minutes past midnight: 5:135:13 a.m. is 313313 minutes past midnight, and 8:358:35 a.m. is 515515 minutes past midnight
step 3
Find the difference in minutes between Jerry's arrival and the first bus: 515313=202515 - 313 = 202 minutes
step 4
Determine how many full 20-minute intervals have passed by dividing 202 minutes by 20: 20220=10\frac{202}{20} = 10 with a remainder of 2 minutes
step 5
Since 10 full intervals have passed, the next interval will be the 11th, which is 20 minutes after the 10th interval
step 6
Calculate the waiting time for the next bus: 202=1820 - 2 = 18 minutes
Jerry will have to wait 18 minutes for the next bus.
Key Concept
Modular Arithmetic and Time Calculation
To find the waiting time for the next bus, we calculate the time elapsed since the first bus and use modular arithmetic to find the remainder, which gives us the time until the next bus arrives.

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