Ryan must read 150

2018 Handbook

2018 Test A Math · Question 38 of 57

Also in 2026 Practice Test A Math, question 33; 2025 Practice Test A Math, question 38.

Question

Ryan must read 150 pages for school this weekend. It took him 30 minutes to read the first 20 pages. At this rate, how much additional time will it take him to finish the reading?

A $2\frac{1}{6}\text{ hr}$
B $3\frac{1}{4}\text{ hr}$
C $3\frac{3}{4}\text{ hr}$
D $7\frac{1}{2}\text{ hr}$

Show the answer

Correct answer: B

Ryan has 130 pages left to read (150 − 20). He read 20 pages in 30 minutes, which means he read at a rate of 40 pages per 1 hour. To find out how much longer it will take him to finish the assignment, divide the total number of pages remaining (130) by the number of pages he is able to read per hour (40):

$\frac{130}{40}=3\frac{1}{4}$

Question analysis

This reading-rate word problem says Ryan read 20 of his 150 pages in 30 minutes and asks how much additional time he needs to finish at that rate. Students must find the pages left, use the rate, and convert minutes to hours. The word 'additional' is easy to overlook.

NYS standards: 6.RP.3b unit rate problems
6.RP.3d converting measurement units
Grade level: Grade 6 content, by NYS standard
Compared with grade 7: At grade 7 Unit rate problems like this are grade 6 content and common in grade 7. It adds a subtraction step and a conversion to hours, and the word 'additional' must be read closely, which keeps it at grade 7 level.
Estimated difficulty: Moderate: several steps, or a close reading with one strong distractor.
Thinking it demands: Depth of knowledge 2, skills and concepts · mainly apply
What makes it hard: Many steps moderate
A very close wrong answer moderate
An answer in an unexpected form minor
Solution: 3 steps
Reading level: Question and choices: about grade 3, 36 words.
Students, last 30 days: Not enough answers yet to show (it takes 10).

Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

The bold word "additional" carries the question, and missing it costs the point even when the rate work is perfect. The rate itself mixes pages, minutes and hours, so students who skip writing units drift into answers that count half-hour blocks or minutes as hours. Subtracting the pages already read before anything else keeps the work on the right quantity.

Many steps moderate Working it out
The solution chains four moves: subtract the 20 pages read, double 20 pages per half hour to 40 per hour, divide 130 by 40, and write the result in hours. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
A very close wrong answer moderate Choosing the answer
The choices 3 1/4 and 3 3/4 hours differ by exactly the half hour already spent on the first 20 pages, so only subtracting those pages first separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
An answer in an unexpected form minor Choosing the answer
A student who works in minutes gets 195 minutes and must convert it to the mixed number 3 1/4 hours to find it among the choices. (Enright, Morley & Sheehan, 2002)

Strategy: Subtract the pages already read, work out how many pages he reads per hour, and divide the remaining pages by that hourly rate.

Traps

Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
Units or scale: The answer is wanted in other units, or a rate or scale must be converted first.

The wrong answers, classified

A Units or scale (King et al., 2004)
Reveals a surface strategy Expected pull: weak
Divides the 130 remaining pages by 60, treating the rate as one page a minute, which gives 2 1/6 hours.
C Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Reveals a slip Expected pull: strong
Times all 150 pages at 40 pages an hour, ignoring the bold "additional", and gets the whole assignment's 3 3/4 hours instead of the time left.
D Units or scale (King et al., 2004)
Reveals partial knowledge Expected pull: moderate
Divides 150 pages by 20 to get 7.5 blocks of reading and reports them as hours, though each 20-page block takes half an hour.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Time from a rate: $t = \frac{p}{r}$; t is the time needed. p is the number of pages to read. r is the rate: the pages read in one hour. Dividing tells you how many hours of reading the pages need.

Sort out what you know
Ryan must read 150 pages in all. He read the first 20 pages in 30 minutes. The word additional is in bold. It means extra time, after the 30 minutes he already spent.
So you need the time for the pages he has not read yet.
Find the pages left
$150 - 20 = 130$
He still has 130 pages to read. Watch out: timing all 150 pages gives $3\frac{3}{4}$ hours, which is choice C. That counts pages he already read.
Find his rate per hour
The choices are in hours, so find how many pages he reads in an hour. 30 minutes is half an hour. In a full hour he reads twice as much:
$20 \times 2 = 40$
His rate is 40 pages per hour.
Divide the pages by the rate
Dividing tells you how many hours the 130 pages take at 40 pages an hour:
$t = \frac{130}{40} = 3\frac{10}{40} = 3\frac{1}{4}$
It will take $3\frac{1}{4}$ more hours. So the answer is B, $3\frac{1}{4}$ hr.

Check your answer

Work in minutes. 130 pages is 6.5 groups of 20 pages. Each group takes 30 minutes, so 6.5 × 30 = 195 minutes. That is 3 hours and 15 minutes. And 15 minutes is a quarter of an hour, so it matches.

The original DOE question

Question 95 as printed on page 88 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 88, question 95. Open page 88 of the handbook (PDF)