Question

If it took Carlos 1/2 hour to cycle from his house to the library yesterday, was the distance that he cycled greater than 6 miles? (Note: 1 mile = 5280 ft)

(1) The average speed at which Carlos cycles from his house to the library yesterday was greater than 16 feet per second.
(2) The average speed at which Carlos cycles from his house to the library yesterday was less than 18 feet per second.

Answer 1

Explanation:

Given

time taken by Carlos to cycle is
`t=0.5\ hr`

For case (1)

Average speed
`v_(avg)>16\ ft/s`

For
`0.5 hr \approx 30* 60=1800\ s`

Distance traveled
`d=1800* 16=28,800\ ft\approx 5.45\ miles`

Therefore Carlos might not be able to cover 6 miles with average speed of 16 ft/s

(2)
`v_(avg)=18\ ft/s`

for 0.5 hr

distance traveled

`d=1800* 18=32,400\ ft\approx 6.136`

Therefore Carlos might be able to cover more than 6 miles with
`18\ ft/s`