Motion Quiz 4
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Question 1 of 13
1. Question
3 pointsTwo cars started from the same point. At 8:00 am the first car traveled West at the rate of 100 km/h. At 9:00 am, the second car traveled South at the rate of 90 km/h. At what time were they 1000 km apart? Round the answer to the nearest whole number
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Question 2 of 13
2. Question
4 pointsThe distance between two cities is 240km. The first half of the trip, the vehicle travels at 100km/hr and then rests for 30 minutes at a gas station. The remainder of the distance the vehicle travels at 80 km/h. What is the average speed of the vehicle, including the time spent resting? Round the answer to the nearest whole number.
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Question 3 of 13
3. Question
4 pointsThe first third of a trip a vehicle travels at 100 km/h. It then rests for the equivalent of a third of the time that it has driven so far. The remainder twothirds of the trip the vehicle travels at 120km/hr. Determine the average speed of the vehicle.
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Question 4 of 13
4. Question
4 pointsThe first third of a trip a vehicle travels at 100 km/h. It then rests for the equivalent of a third of the time that it has driven so far. The remainder twothirds of the trip the vehicle travels at 120km/hr. Determine the average speed of the vehicle.
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The distance between the start and end of the trip is equal to S. The time it takes to travel the first third of the trip (S/3) with 100 km/h is equal to S/300. Rest time, which is a third of the first part of the trip is equal to S/ 900. The time it takes to travel the last part of the trip, which is twothirds of the total distance, is equal to 2S/ (3*120) =S/180. The total time T it takes to travel the full distance is equal to T_{total}= S/300 + S/900) + S/180=S/100. Therefore, average speed V is can be found as S/T_{total}=100km/h.

Question 5 of 13
5. Question
4 pointsThe car travels a distance of S km in T hours with a speed equal to V km/hour. If the speed increases by 20%, then the moving time becomes T1. Find T value.
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Question 6 of 13
6. Question
4 pointsDriver knows: To get at the time from Toronto to Pearson airport he has to drive with a rate more than V_{0}= 50 km/h. However first half of the route was very busy, and he traveled with a speed equal to V_{1}=30 km/h. Second part of the route he traveled with a speed V_{2}=100 km/h. Does he get at the time the airport? Please say:
yes
or
no
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Question 7 of 13
7. Question
4 pointsA traveler passed 10 km and stopped to lunch. After a half an hour he continued to move with increased of 1 km/h speed and reached the destination without delay. Find the initial speed of the traveler, if the first part of the way before lunch is equal to 50% of the entire route.
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Solution : Because the first part of the way before lunch (10 km) is equal to 50% of the entire route the entire route is equal 20 km. Let’s assume that initial speed rate is X. After lunch during the moving his speed was equal to (X+1) km/h. The time of moving before lunch 10/X, after lunch 10/(X+1). The total time is equal to T=10/X+1/2+10/(X+1). This relationship is equal to 20/X, because he arrived to destination without delay. So,
.
This equation is an equivalent to the following:
Positive root solution is X=4.
Answer : Initial speed rate is 4 km/h.

Question 8 of 13
8. Question
3 pointsFirst half of the distance freight train travels at a speed of V km/h. Then automatic railway signaling system stops a train for two hours. After a stop train run at a speed of
(V +10) km/h and arrives to the destination without a delay. Find the speed V value, if without stoppages train at a speed (V10) km/h covers all the way by 6 hours later compared with a trip at a speed of V.
Please, insert the answer without measurement units, for example 100 (instead of 100 km/h)
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Question 9 of 13
9. Question
3 pointsThe attached picture shows cars moving in different direction at an intersection. The traffic density of cars moving in direction 1 (labeled by arrow 1) is equal to 25 cars a minute and 80 cars a minute in direction 2. The traffic light for cars traveling in direct 1 has a green light for 2 minutes straight until it turns yellow. How long in your opinion must the green light be on for cars traveling in direction 2?
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Solution: Since the traffic density of cars in direction 2 is higher than direction 1 by 3.5 times, the green light in direction 2 must be on 3.5 longer than in direction 1, i.e. 2×3.5=7 minutes. Answer: 7 minutes.

Question 10 of 13
10. Question
3 pointsProblem: An airplane makes a round trip from point A to point B and back. During the flight there is a constant wind speed of 25 km/h from point A to point B. What is the ratio between the times it takes the airplane to travel one way versus the time it takes it to fly back to point A? Round to the answer to the nearest tenth decimal.
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Question 11 of 13
11. Question
3 pointsA woman is walking down a downwardmoving escalator and counted n1=100 steps to reach the bottom. Then she runs back up the downward moving escalator at a same speed and covers 300 steps in reaching the top. How many steps n does she cover on the escalator when it is switched off (does not move)?
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Question 12 of 13
12. Question
4 pointsProblem : A motorboat running river upstream, lost a bottle under a bridge. A passenger noticed it 15 minutes later, turned back and discovered the bottle 2 kilometres from the bridge. Find the water’s rate?
Please, insert an answer without measurement units, for example, 20 instead 20 km/h.
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Solution : Let’s say X km/h is a rate of the motorboat in still water, Y km/h is the speed of still water. Moving upstream the boat traveled 1/4×(ХY) km from a bridge in 15 min (1/4 of hour), when passenger discovered that he lost the bottle. He turned back and traveled 1/4×(ХY)+2 km at a rate Х+Y km/h in time

Question 13 of 13
13. Question
3 pointsProblem : Cities A and B located along a river are S km apart. A boat travels downstream from A to B in time t_{1} and back from B to A upstream in time t_{2}. Total time is equal T_{1}=t_{1}+t_{2}. If a boat travels from A to B and back from B to A in still water in total moving time is T_{2}. What time is less T_{1} or T_{2}?
A: T_{1}<T_{2}
B: T_{1}>T_{2}
C: T_{1}=T_{2}
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