Question

john ran the 100-m dash with a time of 9.82 sec. if this pace could be maintained for an entire 26-mi marathon, what would his time be? (notice that 1 m ≈ 3.281 ft and 1 mi = 5280 ft.) his time would be \\(\square\\) hr, \\(\square\\) min, \\(\square\\) sec. (round the final answer to the nearest integer. round all intermediate answers to the nearest integer as needed.)

Explanation:

Step1: Convert marathon distance to meters

First, convert 26 miles to feet: \(26\ \text{mi} \times 5280\ \text{ft/mi} = 137280\ \text{ft}\). Then convert feet to meters: \(\frac{137280\ \text{ft}}{3.281\ \text{ft/m}} \approx 41841\ \text{m}\) (rounded to nearest integer).

Step2: Find John's speed in m/s

Speed \(v = \frac{100\ \text{m}}{9.82\ \text{sec}} \approx 10.18\ \text{m/s}\) (rounded to two decimal places).

Step3: Calculate time for marathon in seconds

Time \(t = \frac{\text{distance}}{\text{speed}} = \frac{41841\ \text{m}}{10.18\ \text{m/s}} \approx 4110\ \text{sec}\) (rounded to nearest integer).

Step4: Convert seconds to hours, minutes, seconds

• Hours: \(4110\ \text{sec} \div 3600\ \text{sec/hr} = 1\ \text{hr}\) (with remainder \(4110 - 3600 = 510\ \text{sec}\)).
• Minutes: \(510\ \text{sec} \div 60\ \text{sec/min} = 8\ \text{min}\) (with remainder \(510 - 480 = 30\ \text{sec}\)).
• Seconds: \(30\ \text{sec}\).

Answer:

1 hr, 8 min, 30 sec