On a bike trip, Rajiv traveled

2018 Handbook

2018 Test B Math · Question 40 of 57

Also in 2026 Practice Test B Math, question 34; 2025 Practice Test B Math, question 40.

Question

On a bike trip, Rajiv traveled 65 kilometers in 5 hours, while Shaina traveled 72 kilometers in 4 hours. How much less was Rajiv’s mean speed, in kilometers per hour (kph), than Shaina’s?

Show the answer

Correct answer: B

Calculate each mean speed:

$R=\frac{65}{5}=13\text{ kph}$

$S=\frac{72}{4}=18\text{ kph}$

Then calculate the difference of both mean speeds:

$S-R=18-13=5\text{ kph}$

Question analysis

Rajiv and Shaina ride different distances in different numbers of hours on a bike trip, and students find how much lower Rajiv's mean speed is, in kilometers per hour. It tests unit rates: speed as distance divided by time. The trap is comparing the raw distances or times instead of the speeds.

NYS standards: 6.RP.3b unit rate problems
6.RP.2 unit rate concept
Grade level: Grade 6 content, by NYS standard
Compared with grade 7: Below grade 7 Unit rates and speed are grade 6 topics, and this needs only two divisions and a subtraction with whole-number results. It is easier than typical grade 7 rate problems, which often involve fractions.
Estimated difficulty: Routine: one familiar step, little to misread.
Thinking it demands: Depth of knowledge 1, recall and reproduction · mainly apply
What makes it hard: Many steps minor
Turning words into math minor
Solution: 3 steps
Reading level: Question and choices: about grade 8, 29 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

Few students miss this one. The risk is subtracting raw numbers from the stem, the distances or the hours, instead of first turning each trip into a speed. Students who write each speed in kilometers per hour before comparing them avoid every wrong choice, and the arithmetic divides evenly.

Many steps minor Working it out
Two divisions, 65 ÷ 5 and 72 ÷ 4, have to be done before the subtraction, so no single operation on the given numbers answers the question. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
Turning words into math minor Understanding the question
"How much less was Rajiv's mean speed" asks for a difference of two rates, while the listed distances and times invite subtracting them directly. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)

Strategy: Divide each rider's distance by their time to get two speeds in kilometers per hour, then subtract the smaller speed from the larger.

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.

The wrong answers, classified

A Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Reveals a surface strategy Expected pull: weak
Subtracts the travel times, 5 − 4 = 1 hour, comparing how long they rode rather than how fast.
C Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Reveals a surface strategy Expected pull: moderate
Subtracts the distances, 72 − 65 = 7 kilometers, which says how much farther Shaina rode, not how much faster.
D Numbers taken from the question (Hegarty, Mayer & Monk, 1995)
Reveals a surface strategy Expected pull: weak
Adds the two travel times, 5 + 4 = 9, a number built from the stem that has nothing to do with either speed.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Speed: $\text{speed} = \text{distance} \div \text{time}$; Distance is how far someone went. Time is how long it took. Speed tells how far they go in one unit of time, like kilometers in one hour. Mean speed is the average speed for the whole trip.

Sort out what you know
Rajiv went 65 kilometers in 5 hours. Shaina went 72 kilometers in 4 hours. Mean speed means average speed. It is measured in kilometers per hour (kph), the distance in one hour. You need how much slower Rajiv was than Shaina.
Find Rajiv’s speed
He went 65 kilometers in 5 hours. Use the speed formula.
$\text{speed} = 65 \div 5 = 13$
Rajiv’s mean speed is 13 kph.
Find Shaina’s speed
She went 72 kilometers in 4 hours. Use the same formula.
$\text{speed} = 72 \div 4 = 18$
Shaina’s mean speed is 18 kph.
Subtract the two speeds
Find how much less 13 is than 18.
$18 - 13 = 5$
Rajiv was 5 kph slower.
Watch out: do not subtract the distances or the times. $72 - 65 = 7$ gives choice C, and $5 - 4 = 1$ gives choice A. Neither one is a speed.
So the answer is B, 5.

Check your answer

Work backward. At 13 kph for 5 hours, Rajiv goes $13 \times 5 = 65$ kilometers. At 18 kph for 4 hours, Shaina goes $18 \times 4 = 72$ kilometers. Both match the question, so the speeds are right.

The original DOE question

Question 97 as printed on page 160 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 160, question 97. Open page 160 of the handbook (PDF)