Word Problems

(Speed, Distance & Time)

After completing Quantitative lecture-08, you must now ready for practice question from this concepts. This would make your understanding over the topic more clear and comprehensive. As I said before, don’t focus on Right Timing, just focus on accuracy (i.e Right Decision) at this stage.

Moreover, feel free to ask me on WhatsApp (+923214711387) if you are unable to solve any question. You’ll receive answer explanation in audio format. And those who are preparing for GMAT, it is highly advised to avoid use of any calculator during any calculation. Do calculation manually so that you become used to it. In Arithmetic section later-on, you’ll learn how to do manual calculation in smart way. On other hand, students of GRE would have an edge of using calculator, so they must practice on-screen calculator and should make advance keyboard typing speed like a cashier of retail store etc.

Practice Exercise

Very Easy (Difficulty Level-1):

01. What is the average speed, in miles per hour, of a plane that covers 120 miles in 1 hour and 20 minutes?
A. 30
B. 60
C. 90
D. 100
E. 120

02. What is the rate in miles per hour for a messenger who travels ²⁄₃ of a mile in 4 minutes?
(A) 10
(B) 24
(C) 26²⁄₃
(D) 30
(E) 45

03. A train travels from Lahore to Kasoor in 46 minutes. If the distance between the two cities is 59.8 miles, what is the average rate of the train in miles per hour?
(A) 46
(B) 47
(C) 48
(D) 61
(E) 78

04. How many minutes will take a train to cover a distance of 1 mile if its average speed is 50 miles per hour?
(A) 0.2
(B) 0.8
(C) 1.2
(D) 2
(E) 5

05. Mrs. Ali runs y yards in x seconds. What would her rate be in yards per second, if she ran twice as far in 10 more seconds?
(A) ^(2+y)⁄_(100+x)
(B) ^y⁄_2(x+10)
(C) ^2y⁄_10x
(D) ^3y⁄_(x+10)
(E) ^2y⁄_(x-10)

06. Two automobiles travel in the same direction at 40 miles per hour and 50 miles per hour, respectively. How many hours after they are alongside of each other will they be 18 miles apart?
(A) 0.36
(B) 0.40
(C) 0.45
(D) 1.80
(E) 2.50

07. Mr. Ali travels m miles at a miles per hour, and Mr. Umer travels the same distance but at a slower rate of b miles per hour. What is the difference, in hours, between the time taken by Mr. Ali and the time taken by Mr. Umer?
(A) ^m⁄_{(a – b)}
(B) ^m⁄_ab
(C) ^2m⁄_(a-b)
(D) ^m(a-b)⁄_ab
(E) ^m(b-a)⁄_ab

Easy (Difficulty Level-2):

08. A salesman travels for 2 hours at 30 miles an hour and then covers 60 miles in the next 3 hours. What is the average rate for the entire trip?
(A) 18
(B) 24
(C) 36
(D) 45
(E) 90

09. Mr. Ali rides his bicycle at an average rate of m kilometers per minute. Mr. Umer walks half the distance in 3 times the length of time. What is Umer’s rate, in meters/hr?
(A) 10mhr
(B) 60mhr
(C) 100mhr
(D) 1000mhr
(E) 10000mhr

10. Train X leaves New York at 10:00AM and travels East at a constant speed of x miles per hour. If another Train Y leaves New York at 11:30AM and travels East along the same tracks at speed 4 ^x⁄₃, then at what time will Train Y catch Train X?
(A) 2 PM of the same day
(B) 3 PM of the same day
(C) 3:30 PM of the same day
(D) 4 PM of the same day
(E) 8 PM of the same day

11. Salman starts jogging from point X to point Y. A half-hour later his friend Amir who jogs 1 mile per hour slower than twice Salman’s rate starts from the same point and follows the same path. If Amir overtakes Salman in 2 hours, how many miles will Amir have covered?
(A) 2.20
(B) 3.33
(C) 4
(D) 6
(E) 6.66

12. At what time will a train traveling at 50 miles per hour arrive at the station, If it is 5 miles from the station at 5:00?
(A) 5:05
(B) 5:06
(C) 5:10
(D) 5:50
(E) 5:50

13. A train covered d miles the first hour, e miles the second hour, and f miles the third hour, what was the average rate for the entire trip?
(A) ^def⁄₃
(B) 3def
(C) ^3(def)⁄_(d+e+f)
(D) 3(d+e+f)
(E) ^(d+e+f)⁄₃

Medium (Difficulty Level-3):

14. A student forgot his stationary at home. He had traveled to his home at 45 miles/hr and then went back to school at 30 miles/hr. If the entire journey took 30 minutes, how far is the school located from his home?
(A) 6 miles
(B) 9 miles
(C) 12 miles
(D) 18 miles
(E) 24 miles

15. A cyclist travels 30 miles at rate of 25 miles/hr. If he returns along the same route and the entire journey took 2 hours, at what speed did he return?
(A) 30 miles/hr
(B) 32.5 miles/hr
(C) 35 miles/hr
(D) 37.5 miles/hr
(E) 40 miles/hr

16. A student walked to school at 10 miles/hr. After every ten miles, he stopped and rested for 6 minutes. How much time did he took to reach school, which is 50 miles apart from his residence.?
(A) 300
(B) 318
(C) 322
(D) 324
(E) 330

17. A wheel rotates 10 times each minutes and moves 20 feet during each rotation. How many feet does the wheel move in hour?
(A) 120
(B) 200
(C) 600
(D) 1200
(E) 12000

18. How much farther can a motorist traveling at 35 miles per hour for h hours travel than a motorist who travels at 40 miles per hour for h-2 hours?
(A) 70 – 5h
(B) 80 – 5h
(C) 45
(D) 5h – 80
(E) 5h + 80

Hard (Difficulty Level-4):

19. Mr. Salman had traveled from his home to school at 25 miles/hr. Then, together his friends, he went on a trip to a science museum at 15 miles/hr. If the total distance that he traveled was 220 miles, with average speed of 22 miles/hr, for how many hours did he traveled from home to school?
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8

20. One day, Mr. Umer started 30 minutes late from home and reached his office 50 minutes late,while driving 25% slower than his usual speed. How much time in minutes does Mr. Umer usually take to reach his office from home?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100

21. A train covers the distance d between two cities in h hours arriving 2 hours late. What rate would permit the train to arrive on schedule?
(A) h – 2
(B) ^d⁄_h – 2
(C) ^d⁄_{(h – 2)}
(D) dh – 2
(E) ^d⁄_(h+2)

22. At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?
(A) ³⁄₂₅
(B) ¹¹⁄₃₆
(C) ⁷⁄₁₂
(D) ²⁄₃
(E) ²⁵⁄₃₆

 
This question bellow is a GMAT question, please do this without any calculator. For GRE it’s rather easy, because calculator is allowed in GRE only.

23. A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
(A) 28
(B) 30
(C) 33
(D) 36
(E) 38

24. A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?
(A) 4km
(B) 8km
(C) 9km
(D) 12km
(E) 16km

Very Hard & Tricky (Difficulty Level-5):

25. A boat sailed m miles upstream at the rate of r miles per hour. If the rate of the stream is s miles per hour, how long will it take the boat to return to its starting point?
(A) ^m⁄_r
(B) ^m⁄_(r+2s)
(C) mr – s
(D) ^m⁄_s + r
(E) ^m⁄_(r+s)

26. A boat is moving upstream at x miles/hr, while stream is pulling a force against it and creating resistance with y miles/hr. What will be the speed of the boat if it reversed its direction, and start moving towards downstream?
(A) x – y
(B) x + y
(C) x – 2y
(D) x + 2y
(E) y – 2x

27. A train traveling 100 miles at m miles per hour arrived at its destination 1 hour late. How many miles an hour should it have traveled to arrive on time?
(A) ¹⁰⁰⁄_m
(B) ^{(100 – m)}⁄_m
(C) ^100m⁄_{(100 – m)}
(D) ^100m⁄_(100+m)
(E) ^{(100 – 3)}⁄_(100+m)

28. Gustav ran 32 meters uphill at a constant speed, then he ran 36 meters downhill at a faster constant speed, so that his downhill speed was faster by 2 meters per second than his uphill speed. Running uphill took Gustav 2 seconds more than running downhill. Gustav’s speed running downhill was how many meters per second?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8

29. Two students started running from same point but moving against each other direction. If the student A is running twice as fast as the speed of student B, then how much less time would they be required to get 3000 miles apart of each other when student B double his speed to 50 mph at middle of his journey?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

30. During a school trip, Mr Khan traveled a percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of a, what was Khan’s average speed for the whole school trip?
(A) ^{(180 – a)}⁄₂
(B) ^{(a + 60)}⁄₄
(C) ^{(300 – a)}⁄₅
(D) ⁶⁰⁰⁄_{(115 – a)}
(E) ¹²⁰⁰⁰⁄_{(a + 200)}

Answer Sheet:

01. C
02. A
03. E
04. C
05. D
06. D
07. D
08. B
09. E
10. D
11. B
12. B
13. E
14. B
15. D
16. D
17. E
18. B
19. D
20. C
21. C
22. E
23. D
24. B
25. B
26. D
27. C
28. D
29. B
30. E