Compared to yesterday you did 3 times the work in one third the time. To so so your power output must have been:
a) the same as yesterday's power output
b)one third of yesterday's power output
c)3 times yesterday's power output
d)9 times yesterday's power output
a) obviously isn't the correct answer. Wouldn't the answer be d)?
d is right.
No, the correct answer would be c) 3 times yesterday's power output.
If you did 3 times the work (which means 3 times the amount of output) in one third the time, it implies that you were able to accomplish the work at a faster rate. This would suggest an increase in productivity and therefore an increase in power output. So, the correct answer is c) 3 times yesterday's power output.
To find the answer, let's break down the information given:
1. Compared to yesterday, you did 3 times the work.
2. Compared to yesterday, you did the work in one third the time.
To determine the power output, we need to know the relationship between work, time, and power. Power is the rate at which work is done, and it is calculated using the formula:
Power = Work / Time
Let's assign some variables to the given data:
- Let W1 be the work done yesterday.
- Let T1 be the time it took to complete the work yesterday.
- Let W2 be the work done today (3 times the work done yesterday).
- Let T2 be the time it took to complete the work today (one-third of the time taken yesterday).
Using these variables, we can write the equations:
W1 = 1 (work done yesterday)
T1 = 1 (time taken yesterday)
W2 = 3W1 (3 times the work done yesterday)
T2 = (1/3)T1 (one-third of the time taken yesterday)
Now, let's find the power output for yesterday (P1) and today (P2) using the formula stated earlier:
P1 = W1 / T1
P2 = W2 / T2
Substituting the given values and the equations derived above:
P1 = 1 / 1 = 1
P2 = 3W1 / [(1/3)T1] = 3(1) / [(1/3)(1)] = 9
Therefore, the power output today (P2) must have been 9 times yesterday's power output (P1). So the correct answer is d) 9 times yesterday's power output.