DO NOT pick 4 days, which would be the middle number between Bob and Gary's rates of 3 and 5 days respectively. The middle rate is the answer that students always want to pick, so the SAT will provide it as an answer to trick you!

Let's think about this intuitively before we actually solve it, so hopefully you won't be tempted to pick a trick answer ever again! Bob can build the house in 3 days if he works by himself, so with someone else helping him, it has to take less than 3 days to build the house! This will always be true. Never pick the middle rate on a combined rates problem like this! 

Now let's look at the problem computationally. Bob can build a house in 3 days, so he builds 1/3 of a house in 1 day. Similarly, Gary can build a house in 5 days, so he builds 1/5 of a house in 1 day. Then together they build 1/3 + 1/5 = 5/15 + 3/15 = 8/15 of the house in 1 day.

Now, just as we did to see how much house Gary and Bob can build separately in one day, we can take the reciprocal of 8/15 to see how many days it takes them to build a house together. (When we took the reciprocal for Bob, 3 days/1 house = 1/3 house per day.) The reciprocal of 8/15 is 15/8, so they took 15/8 days to build the house together. 15/8 days is almost 2 days, which seems like a reasonable answer. Make sure your answer choices make sense when you are solving word problems!

Take the total distance travelled (600 miles) and divide it by the total time travelled (6.5 hrs + 5.5 hrs = 12 hours) = 50 miles/hour 

Call the cars “Car A” and “Car B”.

The least common multiple for the travel time of Car A and Car B is 120. We get the LCM by factoring. Car A’s travel time gives us 3 * 2 * 5; Car B’s time gives us 2 * 2 * 2 * 5.  The smallest number that accommodates all factors of both travel times is 2 * 2 * 2 * 3 * 5, or 120. There are 60 minutes in an hour, so 120 minutes equals two hours. Two hours after 1:00pm is 3:00pm.

If Jon is driving at 10 feet per second he covers 10 * 60 feet in one minute (600 ft/min). In order to determine how far he travels in thirty minutes we must multiply 10 * 60 * 30 feet in 30 minutes.

There are 60 seconds in a minute and 60 minutes in an hour, therefore 3600 seconds in an hour. The arrow will travel 3600x10= 36,000 meters in an hour.

Using the rate formula:  Distance = Rate x Time,

Since Jack’s speed was 7 mph, Jack completed the course in 3 hours

21 = 7 x t

t = 3

Sam’s speed was half of Jack’s speed: 7/2 = 3.5

21 = 3.5 x t

t = 6

Therefore it took Sam 3 hours longer to run the course.

Algebraic solution:  First, convert minutes to hours. 

60/15 = 4, so there are 4 15-minute increments in each hour. Therefore, 4x ounces of water are collected each hour.  Multiply by h to get 4xh as the solution

Plug-in method:  Just choose numbers.

x = 2

h = 3

If 2 ounces drip in 15 minutes, how many ounces will drip in one hour?

2/15 = x/60

15x = 120

x = 8

If 8 ounces drip in one hour, how many ounces will drip in 3 hours? (remember we chose that h = 3)

3 x 8 = 24    

This is the answer we are looking for.

Plug x = 2, and h = 3 into each answer choice, to determine which will work.  Remember you must plug into every answer choice in case more than one works.  In that case, choose different values for x and h, and plug into only the choices that worked the first time.

If Mark makes 15 snowballs in 30 minutes, he can make 30 snowballs in an hour. Working together they can 50 snowballs in one hour. 150 snowballs divided by the amount they can make in one hour (50) will give us the total time it will take them to make 150 snowballs. In this case, 3 hours.

We first use the data for car X to conclude that car X went 40 miles (4gallons*10mi/gallon). We then use 40 miles for car Y, and divide 40 by 8, to give us 5 gallons of gas.

Since the kids are trying to do their chores in one fifth of the time, they need five times as many people. Since they have two, five times as many would be ten. We subtract the two of them and that would mean they need 8 more people, giving us answer 8.