At 8 a.m., Ryan left Town A and cycled towards Town B at 12 km/h. At the same time, Scott left Town B and cycled towards Town A at 16 km/h along the same road.

Question

At 8:30 a.m., they were still 4 km apart. Find the distance between the two towns.

Answer 1

Let r = Ryan's speed

Let s = Scott's speed

 

We know that distance = rate*time

 

The time in this case is 30 minutes, or half of an hour. To avoid having to convert to hours later, we can just use 0.5 for the time.

 

So,

 

0.5r = Ryan's distance

 

And,

 

0.5s = Scott's distance

 

We also know that at the end of this half hour, they were still 4 km apart, so:

 

0.5r + 0.5s + 4 = distance between the towns

 

Now we simply plug in each boy's speed:

 

0.5(12) + 0.5(16) + 4

6 + 8 + 4

= 18

 

So the distance between the 2 towns is 18km