someone can mow his lawn in 48 minutes. if his daughter helps, they can do it in 40 minutes, how long would it take for his daughter to mow the lawn by herself?
someone's rate = 1/48
daughter's rate = 1/x
combined rate = 1/48 + 1/x
= (x + 48)/(48x)
so 1/[(x + 48)/(48x) ] = 40
cross-multiply
40x + 1920 = 48x
8x = 1920
x = 240
slow daughter, testing answer
someone's rate = 1/48
daughter's rate = 1/240
combined rate = 1/48 + 1/240 = 1/40
time at combined rate = 1/(1/40) = 40
it will take the daughter 240 minutes to do the job by herself.
The total resistance of two circuits in parallel is 15 ohms and one circuit has five times the resistance of the other, find the resistance of each circuit. Use 1/R=1/R1+1/R2. R1 and R2 are two individual resistances.
a)Find the smaller resistance
b)Find the larger resistance
To solve this problem, we can use the concept of "work rate." Let's assume that the work to mow the lawn is considered as 1 unit.
If someone can mow the lawn in 48 minutes, their work rate would be 1/48 units per minute.
If the person's daughter helps, they can complete the work in 40 minutes. Let's say the daughter's work rate is "D" units per minute, then the combined work rate of the person and their daughter would be 1/40 units per minute.
Using these work rates, we can set up the equation:
1/48 + D = 1/40
To find D, we can solve the equation.
1/48 + D = 1/40
First, let's find a common denominator for 48 and 40, which is 480:
(480/48)(1/48) + D = (480/48)(1/40)
10/480 + D = 12/480
10 + 480D = 12
480D = 12 - 10
480D = 2
D = 2/480
D = 1/240
So, the daughter's work rate is 1/240 units per minute.
To find how long it would take for the daughter to mow the lawn by herself, we can set up another equation:
D * T = 1
Where T represents the time it takes for the daughter to mow the lawn alone.
Using the daughter's work rate of 1/240 units per minute:
(1/240) * T = 1
Multiplying both sides by 240:
T = 240
Therefore, it would take the daughter 240 minutes to mow the lawn by herself.
To solve this problem, we can use the concept of work rate.
Let's assume that the rate at which the person mows the lawn alone is "P" (rate is measured in lawns per minute). So, in 48 minutes, the person can complete 1 lawn.
Now, if the person's daughter helps, we need to consider their combined work rate. Let's assume the daughter's rate is "D" (also measured in lawns per minute). Together, their combined work rate is P + D.
According to the given information, when they work together, they can complete 1 lawn in 40 minutes.
Using the concept of work rate, we can set up the following equation based on the formula "Work = Rate × Time":
1 = (P + D) × 40
Simplifying this equation, we have:
P + D = 1/40
Since we know that the person's work rate alone is P = 1/48 (because it takes them 48 minutes to complete the lawn alone), we can substitute this value into the equation:
1/48 + D = 1/40
To find the daughter's work rate, we can subtract 1/48 from both sides of the equation:
D = 1/40 - 1/48
Now, let's find a common denominator to simplify the equation:
D = (12/480) - (10/480)
D = 2/480
Simplifying further, we have:
D = 1/240
Therefore, the daughter's work rate is 1/240 lawns per minute, meaning she can mow 1/240th of a lawn per minute.
To find out how long it would take for the daughter to mow the lawn alone, we can use the equation:
1 = (1/240) × T
Where T represents the time it takes for the daughter to mow the lawn alone.
Simplifying this equation, we have:
T = 240 minutes
So, it would take the daughter 240 minutes (or 4 hours) to mow the lawn by herself.