SOLVING PROBLEMS INVOLVING AVERAGE SPEED

Problem 1 :

A car covers a distance of 150 miles in 2 1/2 hours. Calculate the average speed of the car in miles per hour.

Solution :

Distance covered = 150 miles

Time taken = 2  1/2 hours

Average speed = Total distance covered/Total time taken

= 150 / (5/2)

= 150 × 2/5

= 60 miles/hour

So, the average speed of the car 60 miles per hour.

Problem 2 :

A dog runs from one side of a park to the other. The park is 80 meters across. The dog takes 16 seconds to cross the park. What is the speed of the dog?

Solution :

Length of park (or) distance to be covered = 80 meters

Time taken = 16 seconds

Average speed = Total distance covered/Total time taken

= 80/16

= 5 seconds

So, the speed of the dog is 5 seconds.

Problem 3 :

A golf cart is driven at its top speed of 27 km/h for 10 minutes. In meters, how far did the golf cart travel?

Solution :

Speed of the gold cart = 27 km/h

Time taken = 10 minutes

 Speed = Distance / Time

27 = Distance /10

27 × 10 = Distance

270 = Distance

So, the distance covered by golf cart is 270 km.

Problem 4 :

Julia travels in an airplane a distance of 3540km. For one- third of the distance, the airplane files at a speed of 720 km/h, and for the rest of the distance, it files at a speed of 800 km/h. How long does the trip take?

Solution :

Julia travels in an airplane distance = 3540km

One third of the distance can be covered at the speed

= 720km/h

1/3 of the distance = (1/3) of 3540

= (1/3) x 3540

= 1180 km

Time taken to cover the distance of 1180 km = 1180/720

= 1.64

After covering 1/3 of the distance, the remaining distance

= 3540 – 1180

= 2360

The remaining speed is being covered with at the speed of 800 km/hr.

Time taken to cover the distance = 2360/800

= 2.95

Total time taken = 1.64 + 2.95

= 4.59

= 4 hours + 0.59(60) minutes

= 4 hours 35 minutes

Problem 5 :

A train travels with a constant speed of 112km/h. How long will it take to travel a distance of 336 km?

Solution :

Speed = 112km/h

Distance = 336 km

Speed = Distance/ Time

112 = 336/Time

Time = 336/112

= 3 minutes

So, 3 minutes a train travel a distance of 336 km.

Problem 6 :

Cindy rides her bike with a constant speed of 16 km/h. How far can she travel in 60 minutes?

Solution :

Speed = 16 km/h

Time = 60 minutes

Speed = Distance/ Time

16 = Distance/60

60 minutes = 1 hour

16 = Distance / 1

Distance = 16(1)

Distance = 16 km

Problem 7 :

Find the speed.

a)  425 inches in 85 seconds

b)  900 miles in 18 hours

c) 870 feet in 15 minutes

d) 3096 meters in 72 seconds

Solution :

a)  

Distance covered = 425 inches

Time = 85 seconds

Time = distance / speed

Speed = distance / time

= 425/85

= 5 inches/seconds

b)  900 miles in 18 hours

Distance covered = 900 miles

Time = 18 hours

= 900/18

= 50 miles/hour

c)

Distance covered = 870 feet

Time = 15 minutes

= 870/15

= 58 feet/minute

d)

Distance covered = 3096 meter

Time = 72 seconds

= 3096/72

= 43 meter/second

Problem 8 :

You walk 5 city blocks in 12 minutes. How many city blocks can you walk in 2 hours?

Solution :

5 blocks = 12 minutes

1 minute = 5/12 blocks

1 hour = 60 minutes

Number of blocks covered in 60 minutes or 1 hour

1 hour = 60 x (5/12)

= 25 blocks

2 hours = 2(25) blocks

= 50 blocks

So, the number of blocks covered is 50 blocks.

Problem 9 :

You and a friend start biking in opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds.

a. How far apart are you and your friend after 15 minutes?

b. After 20 minutes, you take a 5-minute rest, but your friend does not. How far apart are you and your friend after 40 minutes? Explain your reasoning

Solution :

Distance traveled by yourself = 108 feet

Time taken = 8 seconds

Speed = Distance / time

= 108/8

Speed = 13.5 feet/second

Distance traveled by your friend = 63 feet

Time taken = 6 seconds

Speed = 63/6

= 10.5 feet/second

a) You and your friend both are travelling in the opposite direction.

Distance traveled by yourself in 15 minutes = 15(13.5)

= 202.5 feet

Distance traveled in 20 minutes = 20(13.5)

= 270 feet

Distance traveled by your friend in 15 minutes = 15(10.5)

= 157.5 feet

After 15 minutes the distance between you and your friend = 202.5 - 157.5

= 45 feet

b)  

Distance traveled by yourself in 40 minutes = 40(13.5)

= 540 feet

Distance traveled by your friend = 40(10.5)

= 420 feet

Distance between you and your friend = 540 - 420

= 120 feet