Distance, Rate, And Time

1.

Two people started from the same point at the same time and traveled in opposite directions. One traveled at 60 mph and the other at 40 mph. How long will it take before the two people are 500 miles apart?
- A.
  
  6 hours
- B.
  
  5 hours
- C.
  
  12 hours
- D.
  
  20 hours
- E.
  
  25 hours
Correct Answer
B. 5 hours

Explanation
The two people are moving away from each other at a combined speed of 60 mph + 40 mph = 100 mph. To find the time it takes for them to be 500 miles apart, we can use the formula distance = speed × time. Rearranging the formula to solve for time, we have time = distance / speed. Plugging in the values, we get time = 500 miles / 100 mph = 5 hours. Therefore, it will take 5 hours before the two people are 500 miles apart.

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2.

A bus entered the freeway and traveled at a constant speed of 40 mph. Two hours later a second bus followed the first bus, entering the freeway from the same point as the first bus, and traveled at a constant speed of 50 mph. How long will it take the second bus to catch up with the first bus?

Correct Answer
8 hours
8 hrs
8 h

Explanation
The second bus is traveling at a faster speed than the first bus, so it will eventually catch up. Since the first bus has a two-hour head start, the second bus will need to cover that distance before it can catch up. The distance covered by both buses will be the same when they meet. Since the first bus is traveling at 40 mph and the second bus is traveling at 50 mph, the second bus will cover the two-hour head start distance in 2 hours (40 mph x 2 hours = 80 miles). Therefore, it will take the second bus an additional 6 hours (80 miles / 50 mph = 1.6 hours) to catch up with the first bus. In total, it will take the second bus 8 hours to catch up with the first bus.

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3.

James drove his car down a mountain road at an average rate of 30 mph and returned over the same road at an average rate of 20 mph. If his trip took 5 hours, how far did he drive down the road before he turned around and drove back?
- A.
  
  1
- B.
  
  2
- C.
  
  3
- D.
  
  4
- E.
  
  5
Correct Answer
C. 3

Explanation
James drove his car down the mountain road at an average rate of 30 mph. Let's assume that the distance he drove down the road before turning around is "x" miles. Since he drove at an average rate of 30 mph, the time it took for him to drive down the road is x/30 hours. He returned over the same road at an average rate of 20 mph, which means the time it took for him to drive back is x/20 hours. The total time for the trip is given as 5 hours, so we can set up the equation x/30 + x/20 = 5. Solving this equation, we find that x = 60. Therefore, James drove down the road for 60 miles before turning around and driving back.

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4.

A plane trip lasted for 5 hours and was 555 miles long. The average speed for the first part was 105 mph. The tailwind picked up, so the remainder of the trip was flown at an average speed of 115 mph. for how long did the plane fly at the first part of the trip?Play sound effects
- A.
  
  3.5 hours
- B.
  
  3 hours
- C.
  
  2.5 hours
- D.
  
  2 hours
Correct Answer
D. 2 hours

Explanation
The plane trip lasted for 5 hours and covered a distance of 555 miles. The average speed for the first part of the trip was given as 105 mph. Therefore, we can calculate the distance covered during the first part by multiplying the average speed by the time taken: 105 mph * x hours = distance. Since the total distance is 555 miles and the remainder of the trip was flown at an average speed of 115 mph, we can subtract the distance covered during the first part from the total distance to find the distance covered during the remainder of the trip: 555 miles - (105 mph * x hours) = distance. Finally, we can solve for x by equating the two expressions for distance and find that x = 2 hours.

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5.

A passenger train leaves the station 2 hours after a freight train leaves the same station. The freight train is traveling 20 mph slower than the passenger train. Then, the passenger train overtakes the freight train in 3 hours. d r t passenger train d r 3 freight train d r – 20 3 + 2 = 5 total --- --- ---The distance is just "d" for both trains because they went __________ counting from the station to wherever they met.

Correct Answer
same distance
the same distance
the same amount of distance
same amount of distance

Explanation
The correct answer is "the same distance". Both the passenger train and the freight train traveled the same distance from the station to the point where they met. This is because the passenger train overtook the freight train in 3 hours, so they must have covered the same distance in that time. Additionally, the distance is represented by the variable "d" for both trains in the given table.

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6.

A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in 4 hours. What is the boat's speed in calm water?
- A.
  
  21 mph
- B.
  
  12 mph
- C.
  
  3.5 mph
- D.
  
  2.5 mph
- E.
  
  1 mph
Correct Answer
A. 21 mph

Explanation
The boat's speed in calm water can be calculated by finding the average speed of the boat during the round trip. The boat travels for a total of 7 hours (3 hours with the current + 4 hours against the current) to cover the same distance. The average speed is calculated by dividing the total distance traveled by the total time taken. Since the distance is the same in both directions, the average speed is equal to twice the speed in calm water. Therefore, the boat's speed in calm water is 21 mph (twice the average speed of 10.5 mph).

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7.

One cyclist is riding at 14 mph and the second is riding at 16 mph. They started at the same time from opposite ends of a course that is 45 miles long. How long after they begin will the two cyclists meet?What should be under the column of distance d for the fast guy to complete the table below? d r t slow guy d 14 t fast guy 16 t total 45 --- ---

Correct Answer
45-d
45 - d
45 -d
45- d

Explanation
The distance column for the fast guy should be represented as 45 - d. This is because the total distance of the course is 45 miles, and the distance covered by the fast guy can be calculated by subtracting the distance covered by the slow guy (d) from the total distance (45).

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Distance, Rate, And Time

Two people started from the same point at the same time and traveled in opposite directions. One traveled at 60 mph and the other at 40 mph. How long will it take before the two people are 500 miles apart?

A bus entered the freeway and traveled at a constant speed of 40 mph. Two hours later a second bus followed the first bus, entering the freeway from the same point as the first bus, and traveled at a constant speed of 50 mph. How long will it take the second bus to catch up with the first bus?

James drove his car down a mountain road at an average rate of 30 mph and returned over the same road at an average rate of 20 mph. If his trip took 5 hours, how far did he drive down the road before he turned around and drove back?

A plane trip lasted for 5 hours and was 555 miles long. The average speed for the first part was 105 mph. The tailwind picked up, so the remainder of the trip was flown at an average speed of 115 mph. for how long did the plane fly at the first part of the trip?Play sound effects

A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in 4 hours. What is the boat's speed in calm water?