PSAT Math Grid-Ins Question 13: Answer and Explanation

Question: 13

Marcia can type 18 pages per hour, and David can type 14 pages per hour. If they work together, how many minutes will it take them to type 24 pages?

Correct Answer: 45

Explanation:

45

The question asks for time it takes to do a certain amount of work at a certain rate, so use the rate formula and pay close attention to the units. The formula is W = RT, in which W is the amount of work done, R is the rate or speed, and T is the time. The question says that Marcia and David work together, so start by finding their combined rate. If Marcia types 18 pages per hour and David types 14 pages per hour, then together they will be able to type 18 + 14 = 32 pages per hour. The total number of pages they need to type is 24. Use the rate formula with 32 as the rate and 24 as the work to get 24 = (32) T. To find the time in hours that it takes Marcia and David to type 24 pages, divide both sides by 32 to get 0.75 hours = T. The question asks how many minutes the work will take, so multiply 0.75 × 60 = 45 minutes. The correct answer is 45.