## Speed: Advanced Word Problems

#### 1. In a 10-km race, Grace ran the first 2 km in

1 |

5 |

What was her average speed for the run?

Total distance =

**10 km**

Let's calculate the total time taken:

Time taken for the first 2 km -->

1 |

5 |

Time taken for the next 6 km -->

6 |

9 |

2 |

3 |

Time taken for the last 2 km -->

2 |

12 |

1 |

6 |

Total time taken =

1 |

5 |

2 |

3 |

1 |

6 |

h

31 |

30 |

**Average speed**= 10 km ÷

31 |

30 |

30 |

31 |

Her average speed for the run was

**9.67 km/h**.

#### 2. Bella is taking an adventurous trip through a jungle.

First, she trekked for 30 minutes into the thick jungle at an average speed of 6 km/h.

Next, she took a boat to cross a lake which rode her at an average speed of 20 km/h for 12 minutes.

For the last part of her trip, she hiked for 2 hours at an average speed of 4 km/h.

Find the total distance she covered on her trip.

**Distance travelled during the first part**

Average speed = 6 km/h

Time taken = 30 min =

h

Distance travelled = 6 km/h ×

h = 3 km

Time taken = 30 min =

1 |

2 |

Distance travelled = 6 km/h ×

1 |

2 |

**Distance travelled during the second part**

Average speed = 20 km/h

Time taken = 12 min =

h

Distance travelled = 20 km/h ×

h = 4 km

Time taken = 12 min =

1 |

5 |

Distance travelled = 20 km/h ×

1 |

5 |

**Distance travelled during the last part**

Average speed = 4 km/h

Time taken = 2 h =

h

Distance travelled = 4 km/h × 2 h = 8 km

Time taken = 2 h =

1 |

5 |

Distance travelled = 4 km/h × 2 h = 8 km

**Total distance travelled**= 3 km + 4 km + 8 km = 15 km

She covered a total distance of

**15 km**on her trip.

#### 3. Eric walked at an average pace of 65 m/min for the first half of the distance to his friend's house.

Calculate his average speed for the second half of the distance if he took a total of 18 minutes to reach his friend's house which was 1.3 km away.

**For the first half**

Distance covered = 1.3 km ÷ 2 = 0.65 km = 650 m

Average speed = 65 m/min

Time taken = 650 m ÷ 65 m/min = 10 min

Average speed = 65 m/min

Time taken = 650 m ÷ 65 m/min = 10 min

**For the second half**

Distance covered = 650 m

Time taken = 18 min − 10 min = 8 min

Average speed = 650 m ÷ 8 min = 81.25 m/min

Time taken = 18 min − 10 min = 8 min

Average speed = 650 m ÷ 8 min = 81.25 m/min

His average speed for the second half of the distance was

**81.25 m/min**.#### 4. Sally and Molly started from the same point at the same time in two different cars and drove on the same route to reach the same destination at average speeds of 40 km/h and 45 km/h respectively.

If the route was 270 kilometres long and if Molly arrived at the destination at 5:30 pm, when did Sally arrive there?

**Time taken by Sally**

= 270 km ÷ 40 km/h

= 6.75 h

= 6 h + 0.75 h

= 6 h + (0.75 × 60) min

= 6 h + 45 min

= 6 h 45 min

**Time taken by Molly**

= 270 km ÷ 45 km/h

= 6 h

Sally took 45 min more than Molly.

45 min after 5:30 pm is 6:15 pm.

Sally arrived at the destination at

**6:15 pm.**

#### 5. Carol and Maya took part in a 20-km cycle race. Carol rode at an average speed of 22 km/h while Maya rode at an average speed of 25 km/h.

How far apart will the two girls be when Maya has covered half the distance?

Time taken by Maya to cover half the distance = 10 km ÷ 25 km/h =

2 |

5 |

Distance covered by Carol in

2 |

5 |

2 |

5 |

Distance between Maya and Carol after

2 |

5 |

The girls will be

**1.2 km**apart when Maya has covered half the distance.

#### 6. James and Lily, who were standing 29.25 km apart, started running towards each other at 0915.

James ran at an average speed of 5.5 km/h while Lily ran at an average speed of 7.5 km/h.

a) At what time did they meet?

b) How much distance had Lily run when they both met?

a) Distance covered by James in 1 h = 5.5 km

Distance covered by Lily in 1 h = 7.5 km

Total distance covered by James and Lily in 1 h = 5.5 km + 7.5 km = 13 km

Time taken to cover 13 km = 1 h

Time taken to cover 29.25 km

= 2.25 h

= 2 h + 0.25 h

= 2 h + (0.25 × 60) min

= 2 h + 15 min

= 2 h 15 min

2 h 15 min after 0915 is 1130.

James and Lily met at

**1130**.

b) Distance run by Lily in 2 h 15 min

= 7.5 km/h × (2 h 15 min)

= 7.5 km/h × 2.25 h

= 16.875 km

Lily had run

**16.875 km**when they both met.

#### 7. What is the speed at which the Earth revolves around the Sun?

Note: Assume the Earth's orbit around the Sun to be circular instead of elliptical.

The radius is the average distance of the Earth from the Sun

≈ 150 000 000 km

= 150 million kilometres

≈ 150 000 000 km

= 150 million kilometres

Time taken by the Earth to make one revolution around the Sun = 1 year

Distance travelled by the Earth around the Sun in 1 year

= the orbit of the Earth

= circumference of the circle or the orbit

= 2 × π × radius

= 2 × 3.14 × 150 000 000 km

= 942 000 000 km

Speed =

=

=

=

=

= 107 534 km/h

≈ 100 000 km/h

So, the Earth revolves around the sun at a speed of about

At this speed, it will take only 9 minutes to travel from Singapore to New York!

Distance travelled by the Earth around the Sun in 1 year

= the orbit of the Earth

= circumference of the circle or the orbit

= 2 × π × radius

= 2 × 3.14 × 150 000 000 km

= 942 000 000 km

Speed =

Distance travelled |

Time taken |

=

942 000 000 km |

1 year |

=

942 000 000 km |

365 days |

=

2 580 822 km |

1 day |

=

2 580 822 km |

24 hours |

= 107 534 km/h

≈ 100 000 km/h

So, the Earth revolves around the sun at a speed of about

**100 000 km/h**.At this speed, it will take only 9 minutes to travel from Singapore to New York!