# How many trips needed?

If I can take two trips to the office within five minutes, how many minutes will 130 trips take?

My attempt:

$$\frac{130\text{ trips}}{2} = 65\text{ trips}$$

$$65 \cdot 5 = 325 \text{ minutes}$$

• What you have done looks good to me. – Gerry Myerson Mar 1 '13 at 1:26
• What about "within" five minutes of each other? I forgot to mention that. – Quaxton Hale Mar 1 '13 at 1:29
• I'm not sure how to interpret "within". Does it mean, it might take you less than $5$ minutes to make two trips? or does it mean you have to wait $5$ minutes between trips? Suppose you go to the office at noon, and come back at 12:01. When do you make the next trip to the office? – Gerry Myerson Mar 1 '13 at 3:08
• I was thinking of it as you can start a trip only when the first one is finished, but in a period of 5 minutes. So, the max. time the first trip would take is 2.5 minutes before the next one starts. – Quaxton Hale Mar 1 '13 at 3:11
• OK, so then you can do a complete trip every 2.5 minutes, so 130 trips in $(130)(2.5)$ minutes, which is the same answer you got: $(130)(2.5)=(65)(2)(2.5)=(65)(5)$. Unless I still don't understand the problem.... – Gerry Myerson Mar 1 '13 at 4:08

Hint: You can say you make $2/5$ of a trip to the office every minute. Now determine how many times this goes into $130$. To arrive at this idea, think about the units and cancellation when you divide/multiply.
Assuming time per trip is for a round trip. At $2.5$ minutes per trip, time to take $130$ trips is $130 * 2.5$ Counting the interstitial $5$ minute intervals, add $(130-1)*5$