**Speed – Opposite Direction (Calculate Time to Meet)**

This math revision note aims to help your child understand how to solve speed problem sums involving two parties travelling in opposite directions and meeting.

Your child will learn to calculate the time needed for 2 objects to meet when they travel towards each other.

In particular, I will be covering the following 2 types of variations:

1 – When the respective speeds and total distance are given (Question 1)

2 – Only time taken by each party is given (Question 2)

**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 (Calculate Time to Meet)__

Mark and Zack started running in opposite directions from the same spot around a 400-m running track. Mark ran at a constant speed of 1.5 m/s and Zack ran at a constant speed of 2.5 m/s. How long did it take for them to meet for the first time on the track? Give your answer in minutes and seconds.

• After 1s, Mark will be 1.5 m away from the starting point whereas Zack will be 2.5 m away from the starting point.

• Find the total distance both Mark and Zack covered in 1 second

1.5 m + 2.5 m = 4 m

• In total, they would have covered 4 m of the track in 1 second.

• For Mark and Zack to finally meet, it means that they would have both covered the entire distance (400 m) together in each of their own direction’s track.

• Find the time taken for both to cover 400 m together.

400 m ÷ 4 m = 100 s

= __1 min 40 s__

• This is also the time taken for them to meet for the first time.

__Question 2 (Calculate Time to Meet with no given speed)__

A car takes 6 hours to travel from Town Y to Town Z. A truck takes 9 hours to travel the same distance. At 7 am, the car started travelling from Town Y to Town Z. At the same time, the truck started travelling from Town Z to Town Y. What time will the car and the truck meet?

• Since it takes the car 6 hours to travel the distance, the car can cover ^{1}⁄_{6 }of the distance in 1 hour.

• So, we can divide the distance into 6 parts.

• We also read that the truck takes 9 hours to travel the distance, so the truck can cover ^{1}⁄_{9} of the distance in 1 hour.

• Just like before, we can divide the distance according to how far the truck can travel in an hour – we can divide the distance into 9 parts.

• Now, we can see that the parts are of different size. To make the parts become the same size, we think of the common multiple of 6 and 9.

• The smallest common multiple of 6 and 9 is… 18!

Multiples of 6: 6, 12, __18__

Multiples of 9: 9, __18__

6 x 3u = 18

In each of the 6 parts, we got to split it into 3 smaller units.

9 x 2u = 18

In each of the 9 parts, we got to split it into 2 smaller units.

• Now, the units are of the same size and it will be easier to solve the problem.

• In 1 hour, the car can cover 3 units of distance while the truck can cover 2 units of distance.

3u + 2u = 5u

• Together, both the car and the truck can cover 5 units of distance in an hour.

• In total, the distance between Town Y and Town Z is 18 units.

• Every 5 units of distance requires an hour.

• To find out how long it takes for both to cover the entire distance, we divide the total distance by the distance covered in an hour.

18 ÷ 5 = 3 3/5 h

= 3 36/60 h

= 3 h 36 min

• From the question, we read that both started at 7 am.

• We can use the timeline to find out the time after 3 h 36 min has passed since 7 am.

• As we can see, the car and the truck will meet each other at **10.36 am**.

**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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