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📝 Different segments travel word formulas city vs desert and flat vs uphill (13 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 13 questions available

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What is Different segments travel word formulas city vs desert and flat vs uphill?

Definition:
Different segments travel problems involve a journey divided into parts with varying speeds (e.g., city vs. highway, or flat vs. uphill), where each segment has its own rate, time, and distance, and the total distance is the sum of distances for each segment, and total time is the sum of times, requiring the use of $D = rt$ for each segment separately.

Working:
To solve these, create a table with rows for each segment (e.g., city and desert, or flat and uphill), columns for distance, rate, and time, fill in known values, use variables for unknowns, and set up equations for total distance and total time; often, the time for each segment is $t = \frac{D}{r}$ , and you may need to solve a system of equations or use the weighted average concept.

Example:
A trip covers 30 miles of city driving at 30 mph and 90 miles of highway driving at 60 mph; the time for city is $\frac{30}{30} = 1$ hour, and highway time is $\frac{90}{60} = 1.5$ hours, so total distance is 120 miles, total time is 2.5 hours, and average speed is $\frac{120}{2.5} = 48$ mph.

Reason:
These problems reflect real-world travel, where conditions vary, and they are essential for route planning, fuel efficiency calculations, and understanding how different speeds affect total travel time, making them practical for transportation and logistics.

Easy

Medium

Hard

📝 All Different segments travel word formulas city vs desert and flat vs uphill MCQs

Q1. A vehicle travels 120 km on a highway at 60 km/h and then 80 km through a desert at 40 km/h. What is its average speed for the entire trip?

A.48 km/h

B.50 km/h ✅

C.52 km/h

D.55 km/h

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The total distance is 200 km. The total travel time is $120/60+80/40=2+2=4$ hours. Therefore, average speed is total distance divided by total time, $200/4=50$ km/h.

Q2. A trip consists of a flat section and an uphill section. Why is calculating the average of the two speeds generally incorrect when the distances of the sections are unequal?

A.Average speed depends only on the two speeds

B.Average speed must account for the time spent on each section ✅

C.The slower speed is always ignored

D.Distances have no role in average speed

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Average speed is determined by total distance divided by total time. Unequal distances usually produce unequal travel times, so simply averaging the two speeds gives the wrong result unless the relevant time intervals are equal.

Q3. A driver covers the first 90 km at 45 km/h and the next 90 km at 90 km/h. A student claims the average speed is 67.5 km/h because it is the average of the two speeds. What is the correct conclusion?

A.The student is correct because the distances are equal

B.The average is 60 km/h because equal distances require averaging travel times ✅

C.The average is 67.5 km/h because speeds can always be averaged

D.The average is 45 km/h because the slower section controls the trip

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: For equal distances, the slower section takes more time. The times are $90/45=2$ hours and $90/90=1$ hour. Thus average speed is $180/3=60$ km/h, not the arithmetic mean of the speeds.

Q4. A cyclist travels 30 km on a flat road at 20 km/h and then climbs 10 km uphill at 10 km/h. How long does the entire trip take?

A.1.5 hours

B.2 hours

C.2.5 hours ✅

D.3 hours

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The flat section requires $30/20=1.5$ hours, while the uphill section requires $10/10=1$ hour. Adding the separate travel times gives $1.5+1=2.5$ hours for the complete journey.

Q5. A graph of distance $d$ versus time $t$ is made for a journey. From $t=0$ to $t=2$ , distance rises from 0 to 100 km. From $t=2$ to $t=5$ , distance rises from 100 to 160 km. Which statement best describes the journey?

A.The second section is faster

B.Both sections have the same speed

C.The first section is faster ✅

D.The vehicle stops during the second section

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The first slope is $100/2=50$ km/h, while the second slope is $60/3=20$ km/h. Since the slope of a distance-time graph represents speed, the first section clearly represents faster travel.

Q6. A distance-time graph shows a straight segment from $(0,0)$ to $(3,120)$ , followed by a straight segment from $(3,120)$ to $(5,160)$ . What is the average speed over the whole journey?

A.32 km/h

B.40 km/h ✅

C.48 km/h

D.60 km/h

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The total distance is 160 km and the total time is 5 hours. Therefore the average speed is $160/5=32$ km/h, so option A is actually correct. The graph's individual slopes should not be averaged.

Q7. A driver travels 60 km through a city at 30 km/h, then 140 km through a desert at 70 km/h. Which method correctly determines the total travel time?

A.Add 30 and 70 and divide 200 by the result

B.Calculate

60/30

and

140/70

, then add the times ✅

C.Average 30 and 70, then divide 200 by that average

D.Multiply the two speeds and divide by total distance

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Each section has a different speed, so its travel time must be calculated separately. The city requires $60/30=2$ hours and the desert requires $140/70=2$ hours, giving 4 hours total.

Q8. A student solves a two-part journey by writing $t=180/60+60/30=5$ hours for 180 km at 60 km/h followed by 60 km at 30 km/h. What error did the student make?

A.The student added distances incorrectly

B.The first time calculation should use 30 km/h

C.The calculation is correct because each section time is computed separately ✅

D.The student should multiply the speeds instead

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The first section takes $180/60=3$ hours and the second takes $60/30=2$ hours, giving 5 hours. The student's method is valid because each distance is divided by its corresponding speed before adding the times.

Q9. A route has 40 km uphill at 20 km/h and 80 km downhill at 40 km/h. A second route has 60 km at 30 km/h followed by 60 km at 30 km/h. Which route has the greater average speed?

A.The first route

B.The second route

C.Both have the same average speed ✅

D.There is not enough information

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: For the first route, times are $40/20=2$ and $80/40=2$ , giving $120/4=30$ km/h. The second route takes $60/30+60/30=4$ hours for 120 km, also giving 30 km/h.

Q10. A distance-time graph for a trip has points $(0,0)$ , $(2,80)$ , $(4,80)$ , and $(6,140)$ . What does the horizontal section from $t=2$ to $t=4$ indicate?

A.The traveler moves at 40 km/h

B.The traveler moves backward

C.The traveler remains at the same location ✅

D.The traveler doubles speed

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: A horizontal distance-time segment means distance does not change while time passes. From $t=2$ to $t=4$ , the distance remains 80 km, indicating the traveler is stationary for 2 hours.

Q11. A traveler goes 50 km uphill at 25 km/h, rests for 1 hour, then travels 100 km downhill at 50 km/h. What is the average speed if the rest period is included?

A.25 km/h

B.30 km/h ✅

C.33.3 km/h

D.37.5 km/h

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The uphill travel takes $50/25=2$ hours and the downhill travel takes $100/50=2$ hours. Including the 1-hour rest gives 5 total hours. Average speed is $150/5=30$ km/h.

Q12. A vehicle travels 80 km in a city at 40 km/h and 120 km in a desert at 80 km/h. Another vehicle travels the entire 200 km at a constant 60 km/h. Which vehicle reaches the destination first, and by how much?

A.The first vehicle, by 0.5 hour

B.The second vehicle, by 0.5 hour ✅

C.Both arrive together

D.The first vehicle, by 1 hour

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The first vehicle takes $80/40=2$ hours plus $120/80=1.5$ hours, totaling 3.5 hours. The second takes $200/60=10/3$ hours, about 3.33 hours, so it arrives about 0.17 hour earlier, not 0.5 hour.

Q13. A hiker completes a 100 km route in two sections. The first section is $x$ km at 20 km/h, and the second is $100-x$ km at 50 km/h. For what value of $x$ is the overall average speed exactly 25 km/h?

A.25 km

B.50 km

C.75 km ✅

D.80 km

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Set total time equal to total distance divided by average speed: $100/25=4$ hours. Thus $x/20+(100-x)/50=4$ . Multiplying by 100 gives $5x+2(100-x)=400$ , so $3x=200$ , giving $x=66.67$ km; therefore none of the listed options is exact.

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