# Logic Question Bus Timetable Frequency of Service [Error in Calculation]

I would like to ask about an answer to a logic question involving a bus service, shown below. So I observed the bus stop at STATION and realised if it runs from 07:59 to 20:59, exactly 13 hours at 10 minute intervals, I calculated how many times a bus leaves station, which was

$$\frac{13 \times60}{10} = 78$$

and likewise from 20:45, where buses run every 15 minutes from STATION

$$\frac{2\times60}{15} = 8$$

So I thought the total number of services run was $78 + 8 = 86$ however I appear to be wrong. The answer is apparently $88$ but I can't seem to arrive to the answer of 88.

Can someone help see me where I went wrong?

Suppose a bus comes every $10$ minutes starting from $8$am until $9$ am, which is exactly $1$ hour. How manu buses come in $1$ hour.

Answer would be $7$.

At $8$am, $8:10$ am, $\ldots,8:50$ am, $9:00$am

Do not forget to count the bus at $8$am.

• Strange question to ask actually, but why is that the case? I understand what you've mentioned but why isn't the bus at 8am included in the initial calculation? Once I have that in my mind, I think the question is solved for me! Many thanks anyway for your answer! Nov 1 '17 at 0:15
• I think the thing is how do we understand subtraction. How many integers are there from $1$ to $5$, most people would answer $5$ and if we just perform subtraction, we just measure the distance between $5$ and $1$, which would be $5-1$ which is not what we want. I believe more people will make mistake if we ask how many integers are there from $2$ to $6$. Nov 1 '17 at 0:20
• Don't you mean division? Because I've done division in my solution? Nov 1 '17 at 0:21
• Well, we can then answer the question of how many even numbers are there from $0$ to $10$ inclusive. $\frac{10-0}{2}=5$ but this is not what we want. we miss out a boundary point. Nov 1 '17 at 0:24
• Oh! Gotcha, we forgot the first part. Right ok, many thanks! Nov 1 '17 at 0:27