Rate, work, and mixture word problem setups and solving approaches tested on the GMAT quantitative section.
36 cards · basic cards · AI-written, checked twice. Edit anything.
- What is the fundamental formula relating distance, rate, and time?
- Distance = Rate × Time
- If two people travel toward each other, how do you find their relative speed?
- Add their individual speeds together
- If two people travel in the same direction and one is faster, what is the relative speed?
- Subtract the slower speed from the faster speed
- In work problems, what does a work rate of 1/5 mean?
- The worker completes one-fifth of the job in one unit of time
- How do you combine work rates when two workers work together on the same job?
- Add the individual work rates
- If Worker A completes a job in 6 hours, what is Worker A's work rate?
- 1/6 of the job per hour
- Workers A and B have rates of 1/4 and 1/6 per hour. What is their combined rate?
- 1/4 + 1/6 = 5/12 of the job per hour
- If a combined work rate is 5/12 per hour, how many hours to complete the job?
- 12/5 hours, or 2.4 hours
- What does concentration mean in a mixture problem?
- The amount of solute (ingredient) divided by the total amount of solution
- How do you find the amount of pure ingredient in a mixture?
- Multiply the concentration by the total amount of solution
- If you mix 10 liters of 40% solution with 15 liters of 60% solution, what equation sets up the pure amount in the final mixture?
- 0.4(10) + 0.6(15) = concentration of final mixture × 25
- In a mixture problem combining two solutions, what principle ensures your equation is correct?
- The total amount of pure ingredient is conserved before and after mixing
- If a 200-liter tank holds a 25% solution and 50 liters are drained, what concentration remains?
- Still 25% (removing solution removes solute and solvent in the same proportion)
- In a work problem, if Worker A completes 1/3 of a job and Worker B completes the rest, what fraction does Worker B complete?
- 2/3 of the job
- Two machines working together complete a job in 8 hours. If Machine A alone takes 12 hours, how long does Machine B alone take?
- 24 hours