Math Snap

STEP 1

What is this asking?
How much does it cost per minute to travel from Nantbridge to Andertown when it's not peak travel time?
Watch out!
We're dealing with different units: miles, pounds, pence, and minutes!
Don't mix them up!
Also, we only care about the off-peak price.

STEP 2

1. Calculate the off-peak ticket price.
2. Calculate the travel time.
3. Calculate the price per minute.

STEP 3

The distance from Nantbridge to Andertown is 164 miles.
The off-peak price is 47 pence per mile.
Let's convert the pence to pounds first.
There are 100 pence in a pound, so 47 pence is equal to $47 \div 100 =$$\$0.47$.

STEP 4

Now, we can multiply the distance by the price per mile to get the total ticket price in pounds.
$$164 \text{ miles} \cdot \$0.47/\text{mile} = \$77.08$$ So, the off-peak ticket price is $77.08.

STEP 5

The trip is on a main line, so the train speed is 86 mph.
We need to find out how long it takes to travel 164 miles at this speed.

STEP 6

Remember, speed is distance divided by time.
We can rearrange this formula to find the time: time is distance divided by speed.
$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

STEP 7

Let's plug in our values:
$$\text{Time} = \frac{164 \text{ miles}}{86 \text{ mph}} \approx 1.91 \text{ hours}$$

STEP 8

We need the time in minutes, not hours.
There are 60 minutes in an hour, so:
$$1.91 \text{ hours} \cdot 60 \frac{\text{minutes}}{\text{hour}} \approx 114.6 \text{ minutes}$$

STEP 9

We know the total ticket price is $77.08, and the travel time is about 114.6 minutes.

STEP 10

To find the price per minute, we divide the total price by the total time:
$$\frac{\$77.08}{114.6 \text{ minutes}} \approx \$0.67/\text{minute}$$

The price per minute for an off-peak ticket from Nantbridge to Andertown is approximately $\$0.67$.