<p>So basically I suck at rates. Can someone tell me a common rule(s) to follow when I see a rate question?</p>
<p>How would I do this problem:
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? </p>
<p>And for distance problems I know the distance=rate*time. As I know it "dirt" d=rt
But I can never get it during the test. For example:</p>
<p>Esther drove to work in the morning at an average speed of 45 mph. She returned home in the evening along the same route and averaged 30 mph. If Esther spent a total of 1 hr commuting to and from work, how many miles did Esther drive to work in the morning?</p>
<p>Can someone tell me how I should set up/attack these types of problems???? PLEASE. TY!</p>
<p>1) In one hour, Sally can paint 1/4 of the house. In one hour, John can paint 1/6 of the house. In one hour, together they can paint 5/12 (1/4 + 1/6) of the house. </p>
<p>5/12 house/hr * x = 1 house
x = 12/5 = 2.4 hrs</p>
<p>2) Here’s a handy formula for these types of problems</p>
<p>2xy/(x+y)</p>
<p>2(30)(45)/(45+30)
= 36 miles total</p>
<p>But we want only half the trip distance, so 36/2 = 18.</p>
<p>She traveled 18 miles there and 18 miles back.</p>
<p>I think a lot of people mix up that formula. That actually determines the average speed. The round trip formula is [2(speed1)(speed2)(total time)] / (speed1 + speed2). So the number you obtained would be 36 miles/hour on average instead of the total distance. This means in a one hour round trip, the total distance is 36 miles; half of the round trip (home to work) is 18 miles.</p>
<p>What happens is that the total time is almost always 1 hour for these SAT rate questions so people get lucky, although they usually don’t understand the concept behind it.</p>
<p>Either average speed when you travel the same distance at two different rates or the round trip distance when the traveling time is 1 hour. There’s no mixing up anything if you understand the concepts behind the formula.</p>
<p>An even faster way to solve this type of problem is to pick the answer that’s slightly below the average of the two rates (here, the choice that’s slightly below 37.5) . This is because the longer time spent at the lower speed will skew the average slightly in the direction of the lower speed.</p>
<p>I wasn’t saying you were wrong by the way. It just seems a bit strange that you showed him a formula that determines average speed, but you don’t explain how that the average speed is also the total distance because total time=1.
Not to be offensive, but your second statement is a bit obvious. I was saying that a lot of people mix it up because had the total time been something other than 1, they would have unknowingly found the average speed, while believing they found the total distance. Therefore, they would get a wrong answer.</p>
<p>But anyways, my issue basically was that you should have said the following because you plugged in numbers that would end up with the units of average speed, but you ended up with the units of the distance. Sorry, it just bothered me, and the topic starter might have been confused when he starts using the formula.
2(30)(45)/(45+30)
= 36 miles/hour -> 36 miles total</p>
