**Distance, Speed, Time Relationship**

This math revision note aims to help your child understand the relationship between distance, speed, and time, so that your child can become proficient in solving questions that require this understanding.

**Before you read on, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.**

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__Example __

A college is holding a 10 km running event. Roger’s running speed is 10 km/h while Helen’s running speed is 5 km/h.

Speed Ratio

Roger | : | Helen |

10 km/h | : | 5 km/h |

2 | : | 1 |

The ratio of Roger’s speed to Helen’s speed is 2:1

For the same distance of 10 km, Roger takes 1 hour while Helen takes 2 hours.

Roger’s speed is 10 km per hour, hence he takes 1 hour to cover 10 km.

(10 km 10 km/h = 1 h)

Helen’s speed is 5 km per hour, hence she takes 2 hours to cover 10 km.

(10 km 5 km/h = 2 h)

Time Ratio

Roger | : | Helen |

1 | : | 2 |

The ratio of Roger’s time taken to Helen’s time taken for the same distance is 1:2.

Notice that Speed and Time are inversely proportional to each other.

In other words,

**The speed ratio is the flip side of Time ratio and vice versa**.

The faster/ the more the speed, the less the time taken.

The slower/ the less the speed, the more the time taken.

__Question__

Abhi took 5 hours to drive from City S to City G. Anwar took 6 hours to drive from City G to City S. Abhi’s driving speed is 10 km/h faster than Anwar’s driving speed. How far was City S from City G?

From the question, we can form the Time Ratio.

Time Ratio

Abhi | : | Anwar |

5 | : | 6 |

With the Time Ratio, we can obtain the Speed Ratio since we know the Speed Ratio is the flip side of the Time Ratio.

Speed Ratio

Abhi | : | Anwar | : | Difference |

6 | : | 5 | : | 1 |

6 u | : | 5 u | : | 1 u |

So, the difference that is 1 unit from the Speed Ratio represents 10 km/h.

With that, we can find one person’s speed first.

1 u = 10 km/h

5 u = 10 km/h x 5 = 50 km/h (Anwar’s speed)

Now we can find the distance between the cities easily by using Anwar’s speed multiplied by his time taken.

50 km/h x 6 h = **300 km**

Alternatively, we can find Abhi’s speed and find the distance using his time taken.

6 u = 10 km/h x 6 = 60 km/h (Abhi’s speed)

60 km/h x 5 h = **300 km**

The distance between the two cities is 300 km.

**Before you go, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.**

**This will be delivered to your email inbox.**

To Your Child’s Success,

Ms Nelly Ke

Math Specialist

Jimmy Maths and Grade Solution Learning Centre

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