M - Rates and work

Two people are 14 miles apart and begin walking towards each other. Person A walks 3 miles per hour, and person B walks 4 miles per hour. How long will it take them to reach each other?

3+4=7mph 7 goes into 14 mph = 2 Whats important is that you know the distance they are from each other.

An empty bucket is filled with paint at a constant rate, and after 6 minutes the bucket is filled to 3/10 of its capacity. How much more time will it take to fill the bucket to full capacity?

3/10 = 6 Quickly you can make 3 into 1 by dividing 6 by 3 giving you 1/10 = 2 Or the usual but longer 3/10=6/x (6x10 = 3X) = (20=X) Then deal with remaining amount in the fraction. 7/10 Either do 7x2 = 14 or (7/10 = x/20) = (10x = 140) x=14

Whats a trick to this also? Malak can paint 2/9 of a room in 40 min. At this rate, how long will it take Malak to paint the entire room. 2hrs 3hrs 4hrs

3hrs Feel free to transfer the fraction over in the usual style, just be aware what units you're working in like mins. Also if 2/9 = 40 min then half of that is 1/9 = 20 min so add that up.

Adding rates (working together) Machine A fills soda bottles at a constant rate of 60 bottles every 12 minutes, and Machine B fills soda bottles at a constant rate of 120 bottles every 8 minutes. How many bottles can both machines working together at their respective rates fill in 25 minutes?

500 60/12mins 120/8mins 25 mins? = Its tempting to see how many times 8mins goes into 25 mins and multiple from there but thats no 100% accurate so you would have remainders and some rounding to do... Instead reduce the production to see how many happen per min. 5 per min 15 per min Combine now! 15+5=20 20x 25 mins = 500

What are relative rate problems? Name the Three types

A subset of multiple rate problems. Bodies moving towards each other Bodies moving away from each other Bodies move in the direction of each other Consider the combine rate strategy.

If two workers are working together to complete a task and you know both their rates, what can you do?

Add/combine rates (worker ones rate)1/3 + (worker twos rate)1/2 =5/6

If one worker is working to complete a task and you know the other is working to disassemble the task what can you do?

Add/subtract combine rates Fills at 3 gallon per min Drains at one gallon per min Fills at 2 gallons per min. 3-1=2

Nicky and Chadi begin running a race at the same time, though Nicky starts the race 36 meters ahead of Chadi. If Chadi runs at a pace of 5 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run by the time Chadi passes him? (A) 15 seconds (B) 18 seconds (C) 25 seconds (D) 30 seconds (E) 45 seconds.

B 18 Seconds Consider this like a "3 gallons in, 2 gallons out = 1 gallon gain" So you can pick and answer and apply but don't. They are asking when will chad catch up and pass Nicky. -Both are moving in the same direction at the same time. -You know nicky has a head start by how much 36. 2 goes into 36 18 times or 18 seconds. (3M+36)=(5m) Plug in for M

Al and Barb shared the driving on a certain trip. What fraction of the total distance did Al drive? (1) Al drove for ¾ as much time as Barb did. (2) Al's average driving speed for the entire trip was ⅘ of Barb's average driving speed for the trip.

C Check yourself! Something from nothing! -You are still combine fractions like you might for a shoe maker or a factory. -So combine what you do know and add the total sum! Do alone then combine what you know. Statment 1 NOPE 3/4 of B = A = Time but thats all you have. Rx3/4=D Statment 2 Nope 4/5 of B = A = Rate 4/5 x T = D Combine Together! Al = 4/5 x 3/4 = 3/5 B = RxT=3/5 3/5+3/5=8/5 8/5 = Total Distance From there you could figure out how to get Al's total distance.

Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 45 minutes, for how many kilometers total did she hike east? (A) 2.25 (B) 2.75 (C) 3.25 (D) 3.75 (E) 4.25

C) 3.25 12(mpk) = 1 Thats Constant 12(Mpk) goes into 2.75 or (11/4) and makes 33 33=2.75 You got to be home in 45 min how much further can you go east for? You know it took you 33mins to get here (2.75mpk) so you have 33 back at the least. Difference of 45 and 33 is 12 which we know = 1! "for how many kilometers total did she hike east?" She has to hike back so she can only do half of it. So only add .50 Also it's total so the 2.75 added to the .50 = C 3.25

Mary, working at a steady rate, can perform a task in m hours. Nadir, working at a steady rate, can perform the same task in n hours. Is m<n ? (1) The time it would take Mary and Nadir to perform the task together, each working at their respective constant rates, is greater than M/2 (2) The time it would take Mary and Nadir to perform the task together, each working at their respective constant rates, is less n/2

D Statement one is sufficient. What does m/2 define? -It means half of the M variable! -Time it would take 2 mary's or M's to make one. -1/2xM= M/2 So this means that if M and N work together they work slower than 2 Marys. -Then n must be slower than mary because the problem indicates that M+N is greater than M/2 -Mary is faster than Nadir. Same logic applies to the second statement.

Alejandro, working alone, can build a doghouse in 4 hours. Betty can build the same doghouse in 3 hours. If Betty and Carey, working together, can build the doghouse twice as fast as Alejandro can alone, how long would it take Carey, working alone, to build the doghouse?

Don't be afraid to treat the fractions/rates as fractions 1/4=A 1/3=B ?=C B+C=2A 2A becomes 1/2 1/3 is subtracted from both sides. Plug and chug Make sure to subtract or add fractions when they are multiplication. 1/6=C

Matching units in the RTD Chart What are the two common mistake everyone makes and what should you do instead.

First People forget to express as one unit of So one minuet, One hour, One second. Do not make it 1/4 of a floor per second. Second Always express distance over time 1 floor to 4 seconds Never 4 seconds to one floor. Also don't forget to convert times. don't do min to seconds.

Did it take a certain ship less than 3 hours to travel 9 kilometers? (1 kilometer = 1,000 meters) (1) The ship's average speed over the 9 kilometers was greater than 55 meters per minute. (B) The ship's average speed over the 9 kilometers was less than 60 meters per minute.

Important to see when they are building a equation without explicitly asking what the variable is. Did it take a certain ship less than 3 hours to travel 9 kilometers? (1 kilometer = 1,000 meters) See the time given 3 hours = time See the distance given 9K or 9000Meteres Now you have R x 3(hrs)=9000 Meters Solve for R Since the meters is judged in mins make the 3 hours 180 mins. 180 goes into 9000 Meters 50 times. R must = 50 or not = 50 Statement 1) makes R > 55 so YES and no possibility of No. 1 is Sufficient Statement 2) r < 60 so the trip could be shorter or longer than 3 hours so Statement 2 is not sufficient.

Basic work problems

Instead of RT=D you do RT=W

When should you consider the combine rate strategy.

Objects moving towards each other One moving at 5mph the other moving at 6mph 5+6=11 Away from each other Two cars increase the distance between themselves at a rate of 30mph and 45 mph. 30+45=75pmh (the distance between them is expanding at the rate of 75mph Same direction Person x and Person Y decrease the distance between themselves at a rate of 8-5=3 mph

Multiple Rates Gmat Rate problems with one or more trip / Traveler / production. Whats the best way to deal with this?

RT=D Relationship Amal runs a 30-mile course at a constant rate of 6 miles per hour. If Cahaya runs the same course at a constant rate and completes the course in 60 fewer minutes, how fast did Cahaya run? Kinda self explanatory Same D and combine Subtract the 60 min as one hour from the 5 hours to make it 4.

Matching units in the RTD Chart What must you do to make sure you get this right? An Elevator operates at a constant rate of 4 seconds to rise one floor. How many floors will the elevator rise is 2 minuets?

RTD Chart means 1 floor/4seconds Convert the min to seconds! 120sec in 2 mins

Twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by 2 days? (A) 2 (B) 3 (C) 4 (D) 6 (E) 9

Rate times Time = Work Rate can be fluid. We can be producing at the rate of 12 machines. Time is 8 days and from this you get the work. 12x8=96 Now you have 12M x 2 = 96 M=4

Rate equation

Rate x Time = Distance Can be manipulated like all equations Distance x 1/Rate = Time Rate = Distance x 1/Time

Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 4 hours. How long would it take for both hoses to fill up two-thirds of the pool? (A) 1 hour 36 minutes (B) 2 hours 24 minutes (C) 5 hours

Really reinforcing the logic here... Make sure you ADD the fractions (like in change the denominators) 1/4 + 1/6 = 5/12 Now 2/3 can be risen to the same denominator to help you understand and make them function together. 5/12=2/3 Get the fraction from this and work it back into 60 seconds. Leaving you with only A as answer choice.

If Lior walks to work at a rate of 4 miles per hour and walks home by the same route at the rate of 6 miles per hour, what is lior's average walking rate for the round trip? What type of problem is this and why?

WEIGHTED AVERAGES! NEVER DO THIS! If something moves over the same distance twice but at different rates each time straight average 4+6=10 2÷10 = 5 (SO Wrong) These will always be weighted averages, the slower trip is weighted at the more important. In order to find the average rate. The total combined distance for the trips. The total combined time for the trips. Then use this formula. Total distance ------------=Average Speed Total Time Use 12 cause the problem doesn't give you a total distance. 4mph = 3hours with 12 distance 6mph = 2hours with 12 distance 24 --=4.8 5