Question

last week, mark arrived at filips house in 200 minutes riding his bicycle. the average speed of his bicycle varies inversely with how long it takes him to make the trip. if mark increases his average speed from 8 miles per hour to 11 miles per hour, about how long will it take him to bicycle to filips house? round to the nearest whole number. (1 point)

64 minutes

67 minutes

2,200 minutes

145 minutes

Explanation:

Step1: Calculate the distance

Since distance = speed×time, first convert 200 minutes to hours. 200 minutes = $\frac{200}{60}=\frac{10}{3}$ hours. The initial - speed $s_1 = 8$ miles per hour and time $t_1=\frac{10}{3}$ hours. So the distance $d=s_1t_1=8\times\frac{10}{3}=\frac{80}{3}$ miles.

Step2: Calculate the new time

The new speed $s_2 = 11$ miles per hour. Using the formula $t=\frac{d}{s}$, and substituting $d = \frac{80}{3}$ miles and $s = 11$ miles per hour, we get $t_2=\frac{\frac{80}{3}}{11}=\frac{80}{33}$ hours.

Step3: Convert the new time to minutes

To convert $\frac{80}{33}$ hours to minutes, multiply by 60. $t_2=\frac{80}{33}\times60=\frac{4800}{33}\approx145.45$ minutes. Rounding to the nearest whole - number, $t_2\approx145$ minutes.

Answer:

145 minutes