Remember d=rt where d = distance, r = rate, and t = time.  In this case, the distance to and the distance from are the same, so we know that

d = r₁ t₁ and d = r₂ t₂

Since r₁ = 40 and r₂ = 60, we can solve for the times and get

t₁ = ^d/₄₀ and t₂ = ^d/₆₀

Average speed is found by total distance over total time, so we get

Multiplying the numerator and denominator by ¹²⁰/_d we get ²⁴⁰/_{(3 + 2)} = 48.

First convert minutes to hours, so 10 minutes is 1/6 hours; then remember distance = rate * time, so distance/time = rate then 3/(1/6) = 18 mph

q is the number of dollars to be earned, d is the amount earned each day, so you divide q by d to get the number of days.

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!

We can solve this with lots of calculations and conversions of laps to miles, etc., or we can look at what the question is really asking. We want to know how far Jake swims in the time it takes Fred to swim two miles. Instead of converting Fred's miles to laps and comparing to Jake's laps, let's just look at how fast the two brothers swim in relation to one another. Fred swims twice as fast as Jake, so in the same amount of time, he will swim twice as far as Jake. Therefore if Fred swims 2 miles, Jake swims 1 mile in the same amount of time.

60 minutes in an hour, 240 minutes in four hours. If 4 liters are poured every 3 minutes, then 4 liters are poured 80 times. That comes out to 320 liters. The tank holds 2,000 liters, so  of the tank is full.

The area of a rectangle is the length , multiplied by the width . Here the area of the lawn in meters squared is:

We found that Laura is mowing 175,000 meters squared at a rate of 20,000 meters squared per hour. 

Plugging in 20,000 for the rate, and 175,000 for the total area gives:

Multiply both sides by the total number of hours:

Now, divide both sides by 20,000: