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📝 Distance formula d=rt (11 MCQs)

📖 From Digital SAT Algebra • 2. Linear Equations And Inequalities • 11 questions available

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What is Distance formula d=rt?

Definition:
The distance formula $d = rt$ relates distance $d$ , rate (speed) $r$ , and time $t$ . It states that distance equals the product of rate and time. This formula is used to solve motion problems where one of the three variables is unknown.

Working:
To find rate, solve $r = d/t$ ; to find time, solve $t = d/r$ . For example, if a car travels 150 miles in 3 hours, $d = 150$ , $t = 3$ , so $r = 150/3 = 50$ mph.

Example:
A train travels 240 miles at a speed of 60 mph. Find the time. Using $d = rt$ , $240 = 60t$ , divide by 60: $t = 4$ hours.

Reason:
This formula is a fundamental real-world application of linear equations, allowing calculation of distance, speed, or time when two are known.

Easy

Medium

Hard

📝 All Distance formula d=rt MCQs

Q1. A cyclist travels at $18$ km/h for $2.5$ hours. Which expression correctly models the distance traveled before calculating the answer?

18+2.5

18(2.5)

✅

18\div2.5

2.5\div18

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The distance is found by multiplying rate by time, so $d=rt=18(2.5)$ . The other operations confuse the roles of rate and time and therefore do not represent the physical situation correctly.

Q2. Two buses leave the same terminal at the same time. Bus A travels at $60$ km/h and Bus B at $72$ km/h. After $3$ hours, how much farther has Bus B traveled?

12

36

km ✅

180

216

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Bus A travels $60(3)=180$ km, while Bus B travels $72(3)=216$ km. Their difference is $216-180=36$ km. Comparing both distances prevents the common error of using only one rate.

Q3. A delivery driver must travel $240$ km. If the average speed is $80$ km/h, which reasoning correctly determines the travel time?

A.Multiply

240

80

, giving

19{,}200

hours

B.Subtract

80

from

240

, giving

160

hours

C.Divide

240

80

, giving

3

hours ✅

D.Divide

80

240

, giving

1/3

hour

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Starting with $d=rt$ , solving for time gives $t=d/r$ . Therefore $t=240/80=3$ hours. Multiplying distance and rate produces incorrect units, while reversing the division gives hours per kilometer instead of hours.

Q4. A student says that traveling $45$ km/h for $4$ hours gives $49$ km because $45+4=49$ . What is the best analysis of the student's error?

A.The student should subtract time from rate

B.The student should multiply rate by time because each hour contributes

45

km ✅

C.The student should divide time by rate because hours are smaller

D.The student should multiply distance by time instead

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The student's mistake is treating rate and time as quantities that can simply be added. A rate of $45$ km/h means $45$ kilometers are covered each hour, so four hours produce $45(4)=180$ km.

Q5. A car travels $150$ km in the first $2$ hours and then $90$ km in the next $1.5$ hours. What is its average rate for the entire trip?

60

km/h

68.6

km/h ✅

72

km/h

80

km/h

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The total distance is $150+90=240$ km and the total time is $2+1.5=3.5$ hours. Thus the average rate is $240/3.5\approx68.6$ km/h. Averaging the two rates directly would ignore unequal time intervals.

Q6. A distance-versus-time graph shows a straight line passing through $(0,0)$ and $(5,300)$ , where time is measured in hours and distance in kilometers. What does the slope represent?

A.The total travel time

B.The starting distance

C.The travel rate of

60

km/h ✅

D.The final distance of

300

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: For a distance-versus-time graph, slope equals change in distance divided by change in time. Here the slope is $300/5=60$ km/h, so it represents the constant travel rate rather than total distance or elapsed time.

Q7. A runner increases speed from $8$ m/s to $10$ m/s while keeping the running time fixed at $30$ seconds. By how much does the distance increase?

20

30

60

m ✅

300

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: At $8$ m/s for $30$ seconds, the runner covers $240$ m. At $10$ m/s for the same time, the distance is $300$ m. The increase is $300-240=60$ m, showing how distance changes proportionally with rate when time is fixed.

Q8. A student calculates the time for a $360$ -km trip at $90$ km/h as $32{,}400$ hours by multiplying $360(90)$ . Which correction best explains why this is wrong?

A.Distance and rate should be added

B.Time is found by dividing distance by rate, so

360/90=4

hours ✅

C.Time is found by multiplying distance by rate after converting kilometers to hours

D.The rate must be divided by distance, giving

1/4

hour

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Since $d=rt$ , isolating time requires division: $t=d/r$ . Therefore $t=360/90=4$ hours. The product $360(90)$ has units of kilometers squared per hour, which cannot represent a time measurement.

Q9. Two distance-time graphs are straight lines from the origin. Graph A reaches $180$ km at $3$ hours, while Graph B reaches $160$ km at $2$ hours. Which conclusion is correct?

A.Graph A represents the faster traveler

B.Graph B represents the faster traveler ✅

C.Both travelers have the same rate

D.There is not enough information to compare their rates

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The slope gives the rate. Graph A has rate $180/3=60$ km/h, while Graph B has rate $160/2=80$ km/h. Therefore Graph B is steeper and represents the faster traveler despite having a smaller displayed distance.

Q10. A train travels $120$ km at $60$ km/h, stops for $30$ minutes, and then travels another $180$ km at $90$ km/h. What is the train's total elapsed time, including the stop?

3.5

hours

4

hours

4.5

hours ✅

5

hours

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The first segment takes $120/60=2$ hours and the second takes $180/90=2$ hours. Adding the $0.5$ -hour stop gives $2+0.5+2=4.5$ hours. Thus the correct choice is $4.5$ hours, not $4$ hours, because elapsed time includes the stop.

Q11. A vehicle must cover $420$ km in $6$ hours. It spends $1$ hour stopped, so it can travel for only $5$ hours. What constant travel rate is required while the vehicle is moving?

70

km/h

75

km/h

84

km/h ✅

90

km/h

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The available moving time is $6-1=5$ hours. Using $d=rt$ , the required rate is $r=d/t=420/5=84$ km/h. Using all six hours would incorrectly ignore the stop and underestimate the necessary moving speed.

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