A car is traveling 55 miles per hour

2018 Handbook

2018 Test A Math · Question 29 of 57

Also in 2026 Practice Test A Math, question 2; 2025 Practice Test A Math, question 2.

Question

A car is traveling 55 miles per hour, and 1 mile = 5,280 feet. Which of the following calculations would give the car’s speed in feet per second?

A $\frac{55\cdot 5280}{1}$
B $\frac{55\cdot 5280}{3600}$
C $\frac{55\cdot 3600}{5280}$
D $\frac{55\cdot 5280}{60}$

Show the answer

Correct answer: B

Divide the rate by the number of seconds in an hour. (Since there are 60 minutes in an hour and 60 seconds in a minute, multiply 60 × 60 = 3,600 seconds in an hour):

$\frac{55}{3600}$ miles per second

Multiply by the number of feet in a mile (5,280):

$\frac{55\cdot 5280}{3600}$ feet per second

Question analysis

This unit conversion question gives a car's speed of 55 miles per hour and asks which calculation expresses it in feet per second. Students have to change miles to feet and hours to seconds in one expression. The tricky part is converting both units at once and keeping each conversion factor on the correct side of the fraction bar.

NYS standards: 6.RP.3d converting measurement units
6.RP.3b unit rate problems
Grade level: Grade 6 content, by NYS standard
Compared with grade 7: At grade 7 Grade 7 students usually convert one unit at a time, such as feet to inches. This item converts both parts of a rate at once, miles per hour into feet per second, and asks students to recognize the right setup.
Estimated difficulty: Straightforward: two steps or one careful reading.
Thinking it demands: Depth of knowledge 2, skills and concepts · mainly apply
What makes it hard: A very close wrong answer moderate
Something you must already know minor
Solution: 2 steps
Reading level: Question and choices: about grade 6, 28 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

Nothing has to be calculated; the work is judging which setup turns miles per hour into feet per second. Students who convert only part of the way find a choice waiting, whether they stop at feet per hour or go from hours to minutes instead of seconds. Tracking which unit each factor cancels, rather than computing, is what the question rewards.

A very close wrong answer moderate Choosing the answer
The answer, 55 · 5,280/3,600, and the choice 55 · 5,280/60 are written identically except for the denominator, so only knowing that an hour has 3,600 seconds, not 60, separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Something you must already know minor Working it out
The stem gives 5,280 feet per mile but not the 3,600 seconds in an hour, which students must build from 60 × 60 themselves. (Anderson & Krathwohl, 2001)

Strategy: Write the speed as 55 miles over 1 hour and multiply by unit fractions such as 5,280 feet over 1 mile, checking that miles and hours cancel and only feet per second remain.

Traps

Units or scale: The answer is wanted in other units, or a rate or scale must be converted first.
Stops one step early: A choice is a number from partway through the solution.

The wrong answers, classified

A Stops one step early (King et al., 2004; Gierl et al., 2017)
Reveals partial knowledge Expected pull: moderate
Converts miles to feet with 55 × 5,280 but never changes hours to seconds, leaving the speed in feet per hour.
C Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Reveals a misconception Expected pull: moderate
Turns both conversion factors upside down, multiplying by 3,600 and dividing by 5,280, so miles and hours never cancel.
D Units or scale (King et al., 2004)
Reveals partial knowledge Expected pull: strong
Divides by 60, converting hours to minutes and stopping there, which gives the speed in feet per minute rather than feet per second.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Speed: $r = \frac{d}{t}$; r is the speed, or rate. d is the distance traveled. t is the time it took. Speed tells how far something goes in one unit of time, so you divide the distance by the time.

Sort out what you know
The car goes 55 miles in 1 hour. One mile is 5,280 feet. You need the speed in feet per second. That means how many feet the car goes in 1 second.
The choices are setups, not numbers. So you only need to pick the right setup. You do not have to work out the final number.
Change the miles to feet
Each mile is 5,280 feet. So 55 miles is 55 groups of 5,280 feet. Multiply to get the distance in feet:
$55 \times 5{,}280$
That is how many feet the car goes in 1 hour. Watch out: if you stop here, you have feet per hour, not feet per second. That is choice A.
Change the hour to seconds
The question gives you miles to feet. It does not give you hours to seconds, so you build that yourself. An hour has 60 minutes, and each minute has 60 seconds:
$60 \times 60 = 3{,}600$
So 1 hour is 3,600 seconds. Watch out: 60 is the number of minutes in an hour, not seconds. Dividing by 60 gives feet per minute. That is choice D.
Divide the distance by the time
Use the speed formula. The distance is 55 × 5,280 feet. The time is 3,600 seconds:
$r = \frac{55 \times 5{,}280}{3{,}600}$
Feet on top and seconds on the bottom give feet per second. Watch out: choice C turns both changes upside down, so the miles and hours never cancel. So the answer is B, $\frac{55 \cdot 5{,}280}{3{,}600}$ .

Check your answer

Estimate. 55 × 5,280 is about 290,000 feet in an hour. Divide by 3,600 seconds and you get about 80 feet each second. A car on a highway covering 80 feet in one second sounds right.

The original DOE question

Question 86 as printed on page 87 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 87, question 86. Open page 87 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).