#### 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

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.
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

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.
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

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

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.
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

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
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

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.
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

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.
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

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.
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 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

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

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

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.
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

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 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

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.