GMAT Word Problem Modeling practice questions

A survey of commuters found that 40% drive to work, while the rest take public transportation. Among those who drive, the average commute time is 45 minutes. Among those who take public transportation, the average commute time is 1.25 times the driving time. Select the average commute time for drivers and the average commute time for public transportation users.

A company sells two products, X and Y. In Q1, product X accounted for $\frac{3}{8}$ of total revenue, while product Y accounted for the rest. In Q2, product X's revenue increased by $\frac{1}{4}$ compared to Q1, and product Y's revenue decreased by $\frac{1}{5}$ compared to Q1. The total revenue in Q1 was $800,000. Select the revenue from product X in Q2 and the percentage change in total revenue from Q1 to Q2.

A shipping company has two routes, Route A and Route B, for delivering packages. Initially, packages on Route A take 12 hours to deliver, while packages on Route B take 18 hours. The company implements a new system that reduces the delivery time on Route A by 25% and increases the delivery time on Route B by 20%. What are the new delivery times for Route A and Route B, respectively?

A factory produces widgets on two assembly lines, X and Y. Initially, Line X produces 40% of total output with a 5% defect rate, while Line Y produces 60% with a 3% defect rate. The factory implements quality improvements that reduce Line X's defect rate by 40% and Line Y's defect rate by 25%. Assume total output remains unchanged.

A survey of 500 commuters analyzed their morning travel times by mode of transportation. The data showed that car commuters had an average time of 42 minutes, while train commuters averaged 38 minutes. If 56% of commuters drove cars and the rest took trains, and the overall average commute time was exactly 40.24 minutes, determine: