Question

You and a friend start biking in opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds. a. To the nearest hundredth of a mile, how far apart are you and your friend after 15 minutes? You and your friend are about miles apart after 15 minutes. b. After 20 minutes, you take a 5-minute rest, but your friend does not. To the nearest hundredth of a mile, how far apart are you and your friend after 40 minutes? You and your friend are about miles apart after 40 minutes.

Answer 1

To find your distance apart, you can convert 15 minutes to seconds because that is what the rate is given in.

15 mins x 60 seconds = 900 seconds.

In 900 seconds, there are 900/8=112.5 groups of 8 seconds. This means there are 112.5 groups of 108 feet.

112.5 x 108 = 12150 feet

12150 feet/5280 feet is approximately 2.3 miles.

For your friend you take 900/6 = 150 groups of 6 seconds.

150 x 63 = 9540 feet

9540 feet/5280 feet = 1.79 miles

1.79 miles + 2.3 miles = 2.09 miles

You and your friend are about 2.09 miles apart after 15 minutes.

B). If you go 2.3 miles every 15 minutes, that means you travel about 0.77 miles every 5 minutes. If you travel 20 more minutes (40-15-5) that would be 0.77x 4=3.07 miles more
3.07 + 2.3 = 5.37 miles after 40 minutes (you).

Your friend travels 1.79 in 15 minutes, so 1.79/3 = 0.6 miles every 5 minutes

0.6 x 5 (5 x 5 = 25 minutes)= 3 miles

1.79 + 3 miles= 4.79 miles (friend)

4.79 + 5.37 = 10.16 miles

You and your friend are about 10.16 miles apart after 40 minutes.