Solving Problems involving Rates, Speed, Distance and Time-Gr 6-Solved Examples

Solved Examples and Worksheet for Solving Problems involving Rates, Speed, Distance and Time

Q1At a fair 4 rides on a horse cost $10. Find the number of rides Andrew enjoyed, if he pays a total of $20.

A. 9
B. 7
C. 8
D. 10

Solutions

Step: 1

Let n be the number of horse rides Andrew enjoyed.

Step: 2

410 = n20

[Write a proportion in terms of ridesamount.]

Step: 3

4 × 20 = 10 × n

[Write the cross products.]

Step: 4

80 = 10n

[Multiply.]

Step: 5

8010 = 10n10

[Divide both sides by 10.]

Step: 6

8 = n

Step: 7

Number of rides Andrew enjoyed is 8.

Correct Answer is : 8

Q2A museum charges $5.50 per person as an entry ticket. If a family paid $44 for the tickets, then find the number of people in the family.
A. 15
B. 8
C. 10
D. 6

Solutions

Step: 1

Let n be the total number of people in the family.

Step: 2

numberentry fee, n44 = 15.50

[Write a possible proportion.]

Step: 3

5.50 × n = 44 × 1

[Write the cross products.]

Step: 4

5.50 n = 44

[Multiply.]

Step: 5

5.50n5.50 = 445.50

[Divide both sides by 5.50.]

Step: 6

n = 8

Step: 7

The total number of members in the family = 8.

Correct Answer is : 8

Q3Sam can walk a distance of 7 km in 3 hours. How long would he take to walk 10.5 km?
A. 5.5 hours
B. 5 hours
C. 4 hours
D. 4.5 hours

Solutions

Step: 1

Let n be the time taken by Sam to cover the distance of 10.5 km.

Step: 2

73 = 10.5n

[Write a possible proportion in terms of distancetime.]

Step: 3

7 × n = 10.5 × 3

[Write the cross products.]

Step: 4

7 × n = 31.5

[Multiply.]

Step: 5

7n7 = 31.57

[Divide both sides by 7.]

Step: 6

n = 4.5

Step: 7

Sam would take 4.5 hours to cover 10.5 km.

Correct Answer is : 4.5 hours

Q4The total number of births in the United States in 3 hours was 900. Find the total number of births in 7 hours if the birth rate remains the same.

A. 2,121
B. 2,200
C. 2,221
D. 2,100

Solutions

Step: 1

Let n be the total number of births in 7 hours.

Step: 2

3900 = 7n

[Write a proportion in terms of hoursbirths.]

Step: 3

3 × n = 900 × 7

[Write the cross products.]

Step: 4

3 × n = 6300

[Multiply.]

Step: 5

3n3 = 63003

[Divide both sides by 3.]

Step: 6

n = 2,100

Step: 7

The total number of births in U.S in 7 hours = 2,100.

Correct Answer is : 2,100

Q5A businessman receives 94 phone calls in 8 hours. At this rate, how many phone calls would he receive in 4 hours?

A. 47
B. 46
C. 48
D. 49

Solutions

Step: 1

Let n be the number of phone calls received by the businessman in 4 hours.

Step: 2

948 = n4

[Write a proportion in terms of callshours.]

Step: 3

8 × n = 94 × 4

[Write the cross products.]

Step: 4

8n = 376

[Multiply.]

Step: 5

8n8 = 3768

[Divide both sides by 8.]

Step: 6

n = 47

Step: 7

The businessman receives 47 calls in 4 hours.

Correct Answer is : 47

Q6Tony's respiration rate is 65 breaths in 5 minutes. At this rate, how many breaths will he take in 25 minutes?
A. 325
B. 346
C. 300
D. 337

Solutions

Step: 1

Let n be the respiration rate of Tony in 25 minutes.

Step: 2

655 = n25

[Write a proportion in terms of Number of breathsminutes.]

Step: 3

5 × n = 25 × 65

[Write the cross products.]

Step: 4

5 × n = 1625

[Multiply.]

Step: 5

5n5 = 16255

[Divide both sides by 5.]

Step: 6

n = 325

Step: 7

Tony will breath 325 times in 25 minutes.

Correct Answer is : 325

Q7Alice can write 8 pages in 27 minutes. At this rate, how many pages can she write in 189 minutes?
A. 56
B. 54
C. 68
D. 63

Solutions

Step: 1

Let n be the number of pages Alice can write in 189 minutes.

Step: 2

827 = n189

[Write a possible proportion.]

Step: 3

27 × n = 8 × 189

[Write the cross products.]

Step: 4

27n = 1512

[Multiply.]

Step: 5

27n27 = 151227

[Divide both sides by 27.]

Step: 6

n = 56

Step: 7

Alice can write 56 pages in 189 minutes.

Correct Answer is : 56

Q8Henry can write 4 pages in 16 minutes. At this rate, how many pages can he write in 48 minutes?
A. 22
B. 17
C. 10
D. 12

Solutions

Step: 1

Let n be the number of pages Henry can write in 48 minutes.

Step: 2

pagesminutes ⇒ 416 = n48

[Write a possible proportion.]

Step: 3

16 × n = 4 × 48

[Write the cross products.]

Step: 4

16n = 192

[Multiply.]

Step: 5

16n16 = 19216

[Divide both sides by 16.]

Step: 6

n = 12

[Simplify.]

Step: 7

Henry can write 12 pages in 48 minutes.

Correct Answer is : 12

Q9Find the cost of 30 books, if 6 books cost $4. Assume each book costs the same.
A. $20
B. $23
C. $24
D. $22

Solutions

Step: 1

Let n be the cost of 30 books.

Step: 2

46 = n30

[Write a possible proportion.]

Step: 3

6 × n = 30 × 4

[Write the cross products.]

Step: 4

6n = 120

[Multiply.]

Step: 5

6n6 = 1206

[Divide both sides by 6.]

Step: 6

n = 20

[Simplify.]

Step: 7

The cost of 30 books is $20.

Correct Answer is : $20

Q10The cost of 9 pastries is $19. Find the cost of 27 pastries.

A. $57
B. $67
C. $114
D. $69

Solutions

Step: 1

Let n be the cost of 27 pastries.

Step: 2

919 = 27n

[Write a possible proportion.]

Step: 3

9 × n = 19 × 27

[Write the cross products.]

Step: 4

9 × n = 513

[Multiply.]

Step: 5

9n9 = 5139

[Divide each side by 9.]

Step: 6

n = 57

Step: 7

The cost of 27 pastries is $57.

Correct Answer is : $57

Q11Tim can walk a distance of 9 km in 4 hours. How long would he take to walk 13.5 km?

A. 5.5 hours
B. 6.5 hours
C. 6 hours
D. 7 hours

Solutions

Step: 1

Let n be the time taken by Tim to walk the distance of 13.5 km.

Step: 2

94 = 13.5n

[Write a possible proportion in terms of distancetime.]

Step: 3

9 × n = 13.5 × 4

[Write the cross products.]

Step: 4

9 × n = 54

[Multiply.]

Step: 5

9n9 = 549

[Divide both sides by 9.]

Step: 6

n = 6

Step: 7

Tim would take 6 hours to walk 13.5 km.

Correct Answer is : 6 hours

Q12There are 14 tables for 56 chairs. How many chairs are needed if there are 112 tables?

A. 438
B. 468
C. 458
D. 448

Solutions

Step: 1

Let n be the total number of chairs.

Step: 2

1456 = 112n

[Write a proportion.]

Step: 3

14 × n = 56 × 112

[Write the cross products.]

Step: 4

14n = 6272

[Multiply.]

Step: 5

14n14 = 627214

[Divide both sides by 14.]

Step: 6

n = 448

Step: 7

448 chairs are needed for 112 tables.

Correct Answer is : 448

Q13Jeff can jog 31 2 miles in 45 minutes. At this rate how many hours will he take to cover 7 miles?
A. 45 minutes
B. 1.5 hours
C. 7 hours
D. 1.25 minutes

Solutions

Step: 1

Time = distance travelledaverage speed

Step: 2

= 7mi3.5 mi / 45mins = 90 mins

Step: 3

It would take him 1.5 hrs to travel 7 mi.

Correct Answer is : 1.5 hours

Q14Charlie works part time and earns $10.75 an hour. If he works for different number of hours (h) each week, which equation helps you to find his weekly pay (p)?
A. p = $10.75h
B. p = h - $10.75
C. h = $10.75 - p
D. h = $10.75p

Solutions

Step: 1

p10.75 = h1

[Write a possible proportion.]

Step: 2

p × 1 = h × 10.75

[Write the cross products.]

Step: 3

p = 10.75 h.

Correct Answer is : p = $10.75h

Q15A printing machine produces 2400 newspapers in 3 hours. At this rate, how many newspapers are produced in 14 hours?

A. 4800
B. 24,000
C. 11,200
D. 8000

Solutions

Step: 1

The number of newspapers produced in 3 hours = 2400

Step: 2

The number of newspapers produced in one hour = 2400 ÷ 3 = 800

Step: 3

The total number of newspapers produced in 14 hours = The total number of newspapers produced in one hour × number of hours

Step: 4

= 800 × 14 = 11200

Step: 5

So, the total number of newspapers produced by the printing machine in 14 hours is 11,200.

Correct Answer is : 11,200

Solved Examples and Worksheet for Solving Problems involving Rates, Speed, Distance and Time

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