Evaluate the expression for p = 5 and q = 6:
pq/2 -q
((5*6)/2) - 6 = 15
Easy to Find, a computer data base, charges $30/h during peak hours to access its records. The charge during off-peak hours is $12/h. Indigo Research was billed $876.00 last month for 40 hours of access time. Using a system of equations, find the number of hours charged for usage during peak times.
Let's call the number of hours during peak hours "x" and the number of hours during off-peak hours "y".
We can set up a system of two equations based on the information given:
x + y = 40 (the total number of hours is 40)
30x + 12y = 876 (the total cost is $876)
Now we can use substitution or elimination to solve for one of the variables.
Let's use substitution and solve for y:
y = 40 - x
Substituting this into the second equation:
30x + 12(40 - x) = 876
30x + 480 - 12x = 876
18x = 396
x = 22
So the number of hours charged for usage during peak times is 22.
To find the number of hours charged for usage during off-peak hours, we can substitute x = 22 into either equation:
y = 40 - x = 18
So Indigo Research was charged for 22 hours during peak times and 18 hours during off-peak times.
A weather plane took to the skies to measure the speed of the jet stream. The plane flew 1920 km with the jet stream as a tail wind. Then, it returned to its original location. The eastbound flight took 2 hours, and the westbound flight took 3.2 hours.
Which system of equations can be used to find the speed of the jet stream and the speed of the plane? What was the speed of the jet stream? (p = plane, w = wind)
Let's let the speed of the plane be "p" and the speed of the jet stream be "w".
When flying with the jet stream as a tailwind, the plane's speed relative to the ground is increased by the speed of the jet stream:
speed with tailwind = p + w
And when flying against the jet stream as a headwind, the plane's speed relative to the ground is decreased by the speed of the jet stream:
speed with headwind = p - w
From the problem statement, we know that:
distance with tailwind = 1920 km
time with tailwind = 2 hours
distance with headwind = 1920 km (since it returns to its original location)
time with headwind = 3.2 hours
Using the formula d = rt (distance equals rate times time), we can set up two equations:
1920 = (p + w) * 2
1920 = (p - w) * 3.2
Simplifying each equation by dividing both sides by the respective coefficient:
960 = p + w
600 = p - w
Now we have a system of two equations:
p + w = 960
p - w = 600
We can solve for p (the speed of the plane) by adding the equations:
2p = 1560
p = 780 km/h
To find the speed of the jet stream (w), we can substitute the value of p into either equation:
p + w = 960
780 + w = 960
w = 180 km/h
Therefore, the speed of the jet stream is 180 km/h.
A master electrician earns $62 per hour. His apprentice earns $40 per hour. The master electrician works 3 hours more than the apprentice. If together they are paid $492, how much does the master electrician earn?
Let's call the number of hours that the apprentice works "x".
According to the problem, the master electrician works 3 hours more than the apprentice, which means he works "x + 3" hours.
We can now set up an equation based on the total amount they are paid together:
62(x + 3) + 40x = 492
Simplifying and solving for x:
62x + 186 + 40x = 492
102x = 306
x = 3
So the apprentice works 3 hours.
To find how many hours the master electrician works, we can use the equation we set up earlier:
x + 3 = 6
So the master electrician works 6 hours.
Finally, we can calculate how much the master electrician earns by multiplying his hourly rate by the number of hours worked:
62 * 6 = $372
Therefore, the master electrician earns $372.