QuestionTrack distances (miles) between railway stations are given below.
\begin{tabular}{lccccr}
& Andertown & Housedon Nantbridge & Broxlake & Marlson \\
\hline Housedon & 45 & & & & \\
\hline Nantbridge & & 37 & & & 56 \\
\hline Prexley & & 73 & & 61 & \\
\hline
\end{tabular}
Tracks marked with an asterisk are main lines. All others are local lines.
Ticket prices are per mile during peak travel and 47 p per mile for off-peak.
Train speeds are 86 mph on the main lines and 57 mph on the local lines.
What is the price per minute of a ticket when travelling off-peak from Nantbridge to Andertown?
Studdy Solution
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 .
STEP 4
Now, we can multiply the distance by the price per mile to get the total ticket price in pounds. 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.
STEP 7
Let's plug in our values:
STEP 8
We need the time in *minutes*, not hours.
There are 60 minutes in an hour, so:
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:
STEP 11
The price per minute for an off-peak ticket from Nantbridge to Andertown is approximately .
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