Thread: couple of word equations that I need to get down by thursday

I really need to understand how to do these equations. similar questions were on the pre-test but these are from the book. I think if I can understand these I will understand the test coming up.

After giving a math test, Yolanda can grade 20 tests in 60 minutes and shawn can do it in 68 min. How long will it take them to grade the tests if they work together?

** Major one I have problems understanding on setup

During an afternoon practice, two football team members took the same amount of time to run sprints of 40 yards and 50 yards, respectively. If one of the football team members ran 2 yards per second faster than the other, find the rate of each team member.

D=r*t I know that 40/r and 50/r+2

*The distance a car can travel varies directly with the amount of gas it carries. On the highway, a car travels 80 miles using 4 gallons of fuel. How many gallons are required to travel 200 miles?

***The one that really kills me

I=P/R

A constant voltage is applied to a circuit that has a variable resistor. Varying the resistance causes the current to vary inversely. At a resistance of 8 OHMS, the current is measured to be 12 AMperes. Find the current when the resistance is 20 OHMS.

I really want to pass this test.

After giving a math test, Yolanda can grade 20 tests in 60 minutes and shawn can do it in 68 min. How long will it take them to grade the tests if they work together?

Yolanda grades 0.33 tests per minute.
Shawn grades 0.294 tests per minute.
Together they grade 0.627 tests per minute.

20 tests/0.627 tests per minute = 31.87 minutes.

During an afternoon practice, two football team members took the same amount of time to run sprints of 40 yards and 50 yards, respectively. If one of the football team members ran 2 yards per second faster than the other, find the rate of each team member.

The difference is 10 yards. If one ran 2 yards per second faster than the total time is 10 yards/ 2 yards per second = 5 seconds.

Slower member = 40 yards/5 seconds = 8 Yards per second
Faster member = 50 yards/5 seconds = 10 Yards per second

The distance a car can travel varies directly with the amount of gas it carries. On the highway, a car travels 80 miles using 4 gallons of fuel. How many gallons are required to travel 200 miles?

80 miles/4 gallons = 20 miles per gallon.
200 miles/20 miles per gallon = 10 gallons

A constant voltage is applied to a circuit that has a variable resistor. Varying the resistance causes the current to vary inversely. At a resistance of 8 OHMS, the current is measured to be 12 AMperes. Find the current when the resistance is 20 OHMS.

I= Current, P= Voltage, R= Resistance

I=P/R or P=IR

We'll find P, and consider it to be constant for the second case.
P=8 Ohms x 12 Amps
P= 96 Volts

Now lets plug P back into I=P/R with the new R
I=96 Volts/20 Ohms
I= 4.8 Amps

I did these all in a rush but I trust my answers.

I checked the back of the book you are right, so basically your just dividing these

I tried that on the pretest so hopefully I got those right. I know I messed up with I=PR that threw me for a loop de loop

But How did you get the 5 seconds for the yards?

Sorry for the lack of in-depth explaination. I normally try to go through things quick on here but here's my best explaination.

During an afternoon practice, two football team members took the same amount of time to run sprints of 40 yards and 50 yards, respectively. If one of the football team members ran 2 yards per second faster than the other, find the rate of each team member.

This is a problem that is made easier when you can imagine it.
Pretend they start running at the same time. After a certain amount of time, person a has ran 40 yards and person b has ran 50 yards.
This means that person b has ran an EXTRA 10 yards than person a.
We know that person b has ran 2 yards per second faster than person a AND 10 yards extra. Since those 10 yards can only be accounted for by the fact that he ran an extra 2 yards per second then we can deduce that they ran for a time of (10 yards/ 2 yards per second = 5 seconds).

To help explain this, you could imagine that at half that time, person b would only be half that extra distance ahead. Sure enough, 2.5 seconds x 2 yards per second = 5 yards.

Its much easier to explain these things with nice drawings :P

Yuh, I can't believe how retarded I am, subtract the 50 and the 40 divide it by the 2 to get 5

Than divide the 50 and 40 and there's the answer. DOH ... and Here I have been staring at this question for hours. lol

Haha, don't be soo hard on yourself

I think this teacher likes torturing us. Okay going to try the pre test in the book now, That was the review.