# Speed – Catching Up

This math revision note aims to help your child understand the Gap and Difference concept and have a good grasp of it, so that your child will become proficient in solving speed problem sums that involve one party catching up with another.

Your child will also learn to calculate the time needed for one object to catch up with the other object.

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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## Question 1 (Catching Up)

Wayne drove from Town A to Town B at a speed of 50 km/h. 2 hours later, Euan left Town A and drove towards Town B at 70 km/h.

a. How long did Euan take to catch up with Wayne?

b. How far away were they from Town A when they met?

a) Firstly, we find the extra distance that Wayne covered before Euan started.

50 km x 2 = 100 km

– This is the distance that Euan needs to catch up with Wayne so that they can meet

Find the additional distance that Euan covers more than Wayne in an hour.
70 – 50 = 20 km

– Every hour, Euan can cover 20 km more than Wayne.

20 km  → 1 h

– In other words, it takes 1 hour for Euan to cover 20 km more than Wayne.

– In order to catch up with Wayne, Euan needs to cover a total of 100 km more than Wayne.

100 km ÷ 20 km = 5 h

Since Euan takes 1 hour to cover 20 km extra à following this rate, it will take 5 hours for Euan to cover the extra 100 km which Wayne had a head start of.

b) We can find how far away they are from Town A when they met using Euan’s speed and time taken.

– Euan travelled at a speed of 70 km/h for 5 hours to meet Wayne.

– Find the distance Euan covered.

70 km x 5 h = 350 km

– Alternatively, we can find the distance from Town A when they met by using Wayne’s speed and time taken.

2 h + 5 h = 7 h

– Wayne has been travelling for 7 hours since the start at a speed of 50 km/h.

– Find the distance Wayne covered.

50 km x 7 h = 350 km

## Question 2 (Calculate Speed)

Pamela and Leila started roller-skating at the same time along a 21-km cycling path. Pamela skated at a speed 2 km/h faster than Leila. When she reached the end of the path, Leila was 6 km behind her. Given that their speeds remain the same throughout the journey, what was Leila’s speed?

– Pamela skated 2 km/h faster than Leila. This means that every hour, Pamela covered 2 km more than Leila.

– In the end, Leila was 6 km behind her. This means that Pamela was 6 km ahead of Leila. So, Pamela has covered a total of 6 km more than Leila.

2 km → 1h

6 km ÷  2 km = 3h

– Every 2 km extra covered by Pamela takes 1 hour. Following this rate, the extra 6 km covered by Pamela will take her 3 hours.

Find the distance Leila travelled for the 3 hours.

21 – 6 = 15 km

– Leila traveled 15 km in 3 hours.

So, we can now find Leila’s speed.

15 km ÷  3 hours = 5 km/h

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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