Video Explanation

Text Explanation

Now, since we're comparing times, we'll need the following formula: 

Let's begin by calculating the time normally spent driving to Townville. We know that the distance is 280 kilometers, and that the speed is x kilometers per hour. So the time normally spent driving to Townville is . 

Now we can calculate today's driving time by taking the distance (280 kilometers) and dividing that by today's speed. We know that today's speed is  as fast as usual, so we know that today's speed is  x. So today's driving time is . 

We can now plug these values into the equation that we made above: 

Now we have an equation that we can solve for x. We can begin by simplifying the first term on the right hand side, to get: 

Next, we'll rewrite each of our fractions so that they have the same denominator. The denominator we'll use is 2x. So for we can multiply the top and the bottom by 2. We'll do the same for . And for , we'll multiply the top and the bottom by x. So we get: 

FAQ:  If she leaves half an hour late, doesn't that mean that you would subtract 1/2 instead of add?

First, start by thinking about which quantity is more and which is less.

Normally, the bus takes 280/x hours to travel its route. Today, the bus travels faster, at a speed of (7/6)x and is able to make the trip in 280/((7/6)x) hours.

280/((7/6)x) hours is less than 280/x hours. We have the same distance (280) divided by a faster rate (7/6)x instead of just x.

How much faster is the bus traveling today? We know that the bus leaves 1/2 hour late and will arrive at the same time if it travels at the faster speed of (7/6)x.

So the time on the road today is 1/2 less than the regular time.

regular time – 1/2 = today's time

Or we can say:

regular time = today's time + 1/2

Remember, today's time is LESS because we are traveling faster in order to make up for starting 1/2 hour late. So it makes sense that, to make the equation equal, we need to add to the smaller quantity—today's time. Today's time is exactly 1/2 hour less than the usual time. We have to account for that time we aren't using today by adding it alongside today's time.