I an taking the SAT this week and I am so screwed. I keep getting these types(and ratio and probability- tips?) of questions wrong on practices. I basically set up a chart for d(distance/amount of sth), v(speed/rate), and t(time) and try to fill it out. I usually fill it out(except for #2) correctly, but I don't know what to do with the results LOL. Thank you(I feel so dumb right now), and I hope you can provide some tips and explanations, and also some good sites explaining the ratio, probability, and word problem sections.

1. A freight train left a station at 12 noon, going north at a rate of 50 miles per hour. At 1:00pm, a passenger train left the same station, going south at a rate of 60 miles per hour. At what time were the trains 380 miles apart?

2. A man drove to work at an avg rate of speed of 60 miles per hour and returned over the same route driving at an avg rate of speed of 40 miles per hour. If his total driving time was 1 hour, what was the total number of miles in the round trip?

3. If x people working together at the same rate can complete a job in h hours, what part of the same job can one person working alone complete in k hours?

t is time after 12 noon

f for freight train
distance f = df = 50 t

p for passenger train
dp = 60 (t-1)

when is dp - df = 300 ?

60(t-1) - 50 t = 380
10 t - 60 = 380
10 t = 440
t = 44 hours
so one day and 20 hours
so 8 am
---------------------------------
total distance = 2d
drove out for time t
drove back for time = 1-t
d = 60 t
d = 40 (1-t)
so
60 t = 40 (1-t)
100 t = 40
t = .4 hour
d = 60*.4 = 24 miles
so
2d = 48 miles round trip
=========================
one man works at 1/(xh) jobs / man hour
so man hours per job = x h
k/(x h) = fraction desired

Don't worry, you're not alone! Word problems involving distance, rate, and time (usually referred to as "DRT" problems) can be tricky, but with some practice and understanding of the concepts, you'll be able to tackle them successfully.

Here's a step-by-step guide on how to approach these types of questions:

1. Understand the problem: Read the question carefully to grasp what is being asked. Identify the given information and what needs to be solved.

2. Identify the variables: In DRT problems, the variables are usually distance (d), rate/speed (r), and time (t). Assign variables to each unknown quantity in the problem. For example, in the first question, let's use d1, r1, and t1 for the freight train, and d2, r2, and t2 for the passenger train.

3. Set up the equations: Use the formula distance = rate × time (d = rt) to set up equations based on the given information. For the first question, the equations are: d1 = r1 × t1 and d2 = r2 × t2.

4. Determine the relationships: Determine the relationships between the variables. In this case, the trains are moving in opposite directions, so their distances are adding up to the total distance apart.

5. Solve the equations: Solve the system of equations using the information given. In the first question, you are given the rates and the time difference between when the trains left. You need to find the time they have been apart to reach a distance of 380 miles.

6. Substitute values and solve: Plug the known values into the equations and solve for the unknowns. In this case, substitute 50 miles per hour for r1, 60 miles per hour for r2, and 380 miles for d1 + d2. Then solve for t1 + t2.

7. Interpret the answer: Once you have the solution, make sure to answer the question as per the units provided (usually in hours or minutes) and check if it is reasonable in the context of the problem.

For ratios and probability questions, understanding the underlying concepts and practicing relevant problem types are essential. You can find resources to help you with these topics on various websites, such as Khan Academy, MathIsFun, and Purplemath. These sites offer step-by-step explanations, examples, and practice problems to enhance your understanding.

Remember, practice is key to improving your skills in these areas. Keep working on similar problems, and don't be discouraged if you make mistakes along the way. Learning from those mistakes will help you grow! Good luck on your SAT!