Final answer:
To find the distance you can bike in 40 minutes, average speed is calculated from the given distances at 10 and 30 minutes. At a constant speed of 15 mph, you would travel 10 miles in 40 minutes.
Step-by-step explanation:
You're asking about how far you can ride your bike in 40 minutes, based on the distances traveled in 10 and 30 minutes. To solve this, we can first calculate your average speed by determining the speed for the initial 10 minutes: you travel 2.5 miles in that time. If there's a constant speed, we can extend this to 30 minutes (which you've done) and 40 minutes, which is the time of interest. For the 30 minute distance, you traveled 7.5 miles, which confirms a constant speed since three times the distance of 10 minutes (2.5 miles) is 7.5 miles.
To find out how far you can ride in 40 minutes, simply calculate the average speed using the distances given and then apply it to the 40-minute time frame. Your average speed is 2.5 miles/10 minutes, which can be converted to 15 miles/60 minutes (or 15 mph). Multiplying the average speed by 2/3 (as 40 minutes is 2/3 of an hour), we get the distance you can travel in 40 minutes:
Distance = Speed × Time
15 mph × (2/3 hour) = 10 miles
Therefore, at this constant average speed, you would travel 10 miles in 40 minutes.