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📝 Solve distance formula for d (12 MCQs)

📖 From Digital SAT Algebra • 2. Linear Equations And Inequalities • 12 questions available

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What is Solve distance formula for d?

Definition:
Solving the distance formula for $d$ means expressing distance as the product of rate and time, which is already given by $d = rt$ . However, if you have other forms like $r = d/t$ , you can multiply both sides by $t$ to isolate $d$ : $d = rt$ .

Working:
Given $r = d/t$ , multiply both sides by $t$ : $r \cdot t = (d/t) \cdot t$ , so $d = rt$ . This is the standard form.

Example:
If a plane flies at 400 mph for 5 hours, find distance. Using $d = rt$ : $d = 400 \cdot 5 = 2000$ miles.

Reason:
Isolating $d$ provides a direct formula to compute distance when speed and time are known, which is frequently needed in travel problems.

Easy

Medium

Hard

📝 All Solve distance formula for d MCQs

Q1. A cyclist travels at a constant rate of 18 km/h for 2.5 hours. Which equation correctly represents the distance traveled?

A.d=18+2.5

B.d=18(2.5) ✅

C.d=18/2.5

D.d=2.5-18

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The distance formula is $d=rt$ , so multiplying the rate 18 km/h by the time 2.5 hours gives 45 km. Addition, subtraction, or division would not preserve the required units for distance.

Q2. A train travels 360 km in 4.5 hours at a constant speed. What is its rate?

A.80 km/h ✅

B.81 km/h

C.84 km/h

D.90 km/h

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Using $r=d/t$ , divide 360 km by 4.5 hours to obtain 80 km/h. However, checking the multiplication $80(4.5)=360$ confirms the result and guards against choosing a nearby value from inaccurate division.

Q3. A delivery driver plans to travel 420 km. If the average rate is increased from 70 km/h to 84 km/h, how much time is saved?

A.0.5 hour

B.1 hour ✅

C.1.5 hours

D.2 hours

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: At 70 km/h, the trip takes $420/70=6$ hours. At 84 km/h, it takes $420/84=5$ hours. The difference is 1 hour, illustrating that for fixed distance, increasing rate reduces travel time.

Q4. A boat travels 96 miles downstream in 3 hours. If the boat's speed relative to the water is 28 mph, what is the downstream current speed?

A.2 mph

B.4 mph ✅

C.6 mph

D.8 mph

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The actual downstream rate is $96/3=32$ mph. Since the boat itself moves at 28 mph relative to the water, the current contributes $32-28=4$ mph. The key is distinguishing total rate from boat rate.

Q5. A student claims that if a car travels 150 km in 2 hours and then 90 km in 1 hour, its average speed is $75+90=165$ km/h. What is the correct average speed?

A.60 km/h

B.70 km/h

C.80 km/h ✅

D.120 km/h

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Average speed must be calculated using total distance divided by total time, not by adding individual speeds. The total distance is 240 km and total time is 3 hours, giving 80 km/h.

Q6. A student solves $240=60t$ by dividing 240 by 60, obtaining $t=4$ hours. Another student obtains $t=180$ by subtracting 60. Which reasoning is valid?

A.Only the subtraction method

B.Only the division method ✅

C.Both methods

D.Neither method

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Since 60 multiplies $t$ , the inverse operation is division. Thus $t=240/60=4$ hours. Subtracting 60 does not undo multiplication, so it changes the equation incorrectly and produces an invalid time.

Q7. A graph of distance versus time is 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.Travel time of 60 hours

B.Distance of 60 kilometers

C.Rate of 60 km/h ✅

D.Rate of 300 km/h

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The slope is change in distance divided by change in time, $300/5=60$ . Because the vertical axis is distance and the horizontal axis is time, the slope has units km/h and represents constant rate.

Q8. A student writes $t=d+r$ when solving a distance-rate-time problem. For $d=180$ km and $r=60$ km/h, the student gets $t=240$ . Why is this reasoning flawed?

A.Time should be found by multiplying distance and rate.

B.Distance and rate have incompatible units for addition. ✅

C.Rate should always be subtracted from distance.

D.The numerical answer should be rounded first.

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Distance has units of kilometers while rate has units of kilometers per hour, so they cannot be meaningfully added. Dividing distance by rate gives $180/60=3$ hours, correctly preserving the time unit.

Q9. A distance-time graph rises from 0 km at 0 hours to 200 km at 4 hours, then remains horizontal until 6 hours. What happened during the horizontal portion?

A.The object moved at 50 km/h.

B.The object moved backward at 100 km/h.

C.The object stopped for 2 hours. ✅

D.The object accelerated for 2 hours.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: A horizontal distance-time graph has zero change in distance while time continues increasing. Therefore, the object's rate is 0 km/h during those two hours, meaning it remained stopped.

Q10. A rescue vehicle needs to travel 500 km. It drives 200 km at 50 km/h and the remaining 300 km at an unknown constant rate. The entire trip takes 7 hours. What is the unknown rate?

A.50 km/h

B.60 km/h

C.75 km/h

D.100 km/h ✅

💡 Difficulty: hard | ✅ Correct: D

📖 Explanation: The first 200 km takes $200/50=4$ hours, leaving 3 hours for the remaining 300 km. Therefore the unknown rate is $300/3=100$ km/h. The calculation requires separating the trip into two stages.

Q11. Two routes have the same total distance of 240 km. Route A can be completed at a constant 80 km/h. Route B requires 60 km/h for half the distance and 120 km/h for the other half. Which route takes less time, and by how much?

A.Route A by 0.5 hour

B.Route A by 1 hour

C.Route B by 0.5 hour

D.Both take the same time ✅

💡 Difficulty: hard | ✅ Correct: D

📖 Explanation: Route A takes $240/80=3$ hours. Route B takes $120/60=2$ hours plus $120/120=1$ hour, totaling 3 hours. Therefore, neither route is faster; they take exactly the same time.

Q12. A spacecraft travels at 12 km/s. A signal indicates that it is 54,000 km from a station. Ignoring any change in speed, how many seconds will the spacecraft need to reach the station, and what is the best justification?

A.4,500 seconds, because

t=d/r

✅

B.648,000 seconds, because

t=dr

C.4,488 seconds, because

t=r/d

D.66,000 seconds, because

t=d+r

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: For fixed distance and rate, time is found by $t=d/r$ . Substituting 54,000 km and 12 km/s gives 4,500 seconds. The units also confirm the result because km divided by km/s produces seconds.

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