Question

Izumi is running on a quarter-mile oval track. After running 110 yards, his coach records his time as 16 seconds.

How fast in miles per hour, was Izumi running for the first 110? There are 1,760 yards in a mile. Explain all of your work

Answer 1

14.04 miles per hour

Explanation:

The problem is asking for Izumi's speed. The formula of speed is:

• s =
  `(d)/(t)` , where "s" means speed, "d" means distance and "t" means time.

The problem is also asking for the unit miles per hour (
`(miles)/(hour)`) so, this means that we have to know how many miles Izumi ran, given that the problem only mentioned yards (110 yards).

Let's convert 110 yards to miles, provided that he Izumi ran 1,760 yards in a mile.

• 110 yards ÷ 1760
  `(yards)/(mile)` = 0.0625 miles (this is the distance covered by Izumi in miles)

Let's go back again to the formula: s =
`(d)/(t)`

s =
`(0.0625 miles)/(16 seconds)` = 0.0039
`(miles)/(sec)`

Since, the we arrived at a miles per second unit, we have to convert it to miles per hour.

So, if a minute has 60 seconds, then an hour has 3,600 seconds.

Thus, 0.0039
`(miles)/(sec)` × 3,600
`(seconds)/(hour)` = 14.04 miles per hour (the answer)