Question

Math

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 $8: 35$ 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: $5:13$ a.m. is $313$ minutes past midnight, and $8:35$ a.m. is $515$ minutes past midnight

step 3

Find the difference in minutes between Jerry's arrival and the first bus: $515 - 313 = 202$ minutes

step 4

Determine how many full 20-minute intervals have passed by dividing 202 minutes by 20: $\frac{202}{20} = 10$ 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: $20 - 2 = 18$ minutes

Answer

Jerry will have to wait 18 minutes for the next bus.

Key Concept

Modular Arithmetic and Time Calculation

Explanation

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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