A clock gains s seconds in one hour. In its simplest form, write down an expression in term of s and d for the number of minutes it gains in d days.
in 1 hour it gains s seconds
in 1 day it gains 24s seconds
in d days it gains 24sd seconds
in d days it gains 24sd/60 minutes
in d days it gains 2sd/5 minutes
Well, I think the clock is on a mission to make time fly! Let's calculate the number of minutes it gains in d days.
In one hour, the clock gains s seconds. Hmm, that's quite a jump for a clock! Now, let's convert this into minutes. We know that there are 60 minutes in an hour, so the clock gains (s/60) minutes in one hour.
Now, if the clock gains (s/60) minutes in one hour, then in 24 hours (which make up a day), the clock will gain (24 × (s/60)) minutes.
But we're not done yet! To calculate the number of minutes the clock gains in d days, we need to multiply the previous result by d. So, in d days, the clock gains d × (24 × (s/60)) minutes.
Now, let's simplify this expression. We have d × (24 × (s/60)) minutes. Since multiplication is associative, we can rewrite this expression as (d × 24 × s)/60.
Therefore, the number of minutes the clock gains in d days is (d × 24 × s)/60. Voilà!
To find the number of minutes the clock gains in d days, we need to consider the following:
1 hour = 60 minutes
1 day = 24 hours
So, the total number of minutes the clock gains in one day can be found by multiplying the number of minutes in one hour (60 minutes) with the number of hours in one day (24 hours):
Total minutes gained in one day = 60 minutes/hour x 24 hours = 1440 minutes
Since the clock gains s seconds in one hour, we can say that the clock gains (s/60) minutes in one hour.
Therefore, the number of minutes the clock gains in d days can be calculated by multiplying the total number of minutes gained in one day with the number of days:
(Number of minutes gained in d days) = (Total minutes gained in one day) x (Number of days)
= 1440 minutes x d
= 1440d minutes
Hence, the expression in terms of s and d for the number of minutes the clock gains in d days is 1440d.
To find the number of minutes the clock gains in d days, we need to calculate the number of hours in d days, and then multiply it by the number of seconds gained per hour.
First, let's calculate the number of hours in d days. Since each day has 24 hours, multiplying d by 24 gives us the total number of hours in d days.
Number of hours in d days = 24 * d
Next, we need to find the number of minutes gained in the calculated number of hours. Since each hour has 60 minutes, we multiply the number of hours by 60.
Number of minutes gained = (24 * d) * 60
Finally, we need to consider the number of seconds gained per hour. Since the clock gains s seconds in one hour, we multiply the number of minutes gained by the number of seconds gained per hour.
Number of minutes gained = ((24 * d) * 60) * s
Therefore, the expression in terms of s and d for the number of minutes the clock gains in d days is ((24 * d) * 60) * s.