QuestionBerechne die Summe: $15684 \, s + 955 \, \min + 8.2 \, h + \frac{13}{72} \, d = \, d \, h \, \min \, s$

Studdy Solution

STEP 1

Assumptions1. The given expression is in terms of seconds (s), minutes (min), hours (h), and days (d). . There are60 seconds in a minute,60 minutes in an hour, and24 hours in a day.

STEP 2

First, we need to convert all the terms into the same unit. Let's convert everything into seconds.
We know that1 minute =60 seconds1 hour =60 minutes =3600 seconds1 day =24 hours =1440 minutes =86400 secondsSo, we can write the given expression in terms of seconds as follows $15684 s+955 \min \times60 s/\min +8.2 h \times3600 s/h +\frac{13}{72} d \times86400 s/d$

STEP 3

Now, let's calculate each term separately.
$15684 s =15684 s$ $955 \min \times60 s/\min =57300 s$ $8.2 h \times3600 s/h =29520 s$ $\frac{13}{72} d \times86400 s/d =15600 s$

STEP 4

Add all the terms together to find the total time in seconds.
$Total\, time =15684 s +57300 s +29520 s +15600 s$

STEP 5

Calculate the total time in seconds.
$Total\, time =15684 s +57300 s +29520 s +15600 s =118104 s$

STEP 6

Now, we need to convert the total time from seconds into days, hours, minutes, and seconds.
First, let's convert seconds into days. We know that1 day =86400 seconds. So, we divide the total time by86400.
$Days = Total\, time /86400$

STEP 7

Calculate the number of days.
$Days =118104 s /86400 =1.367 d$

STEP 8

Now, let's convert the remaining part of days into hours. We know that1 hour =3600 seconds. So, we multiply the decimal part of days by86400 and then divide by3600.
$Hours = (Days - floor(Days)) \times86400 /3600$

STEP 9

Calculate the number of hours.
$Hours = (.367 d - d) \times86400 /360 =8.808 h$

STEP 10

Now, let's convert the remaining part of hours into minutes. We know that minute =60 seconds. So, we multiply the decimal part of hours by3600 and then divide by60.
$Minutes = (Hours - floor(Hours)) \times3600 /60$

STEP 11

Calculate the number of minutes.
$Minutes = (8.808 h -8 h) \times3600 /60 =48.48 min$

STEP 12

Finally, let's convert the remaining part of minutes into seconds. We multiply the decimal part of minutes by60.
$Seconds = (Minutes - floor(Minutes)) \times60$

STEP 13

Calculate the number of seconds.
$Seconds = (48.48 min -48 min) \times60 =28.8 s$ So, the solution is day,8 hours,48 minutes, and29 seconds (rounding up the seconds).

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