Question

problem solving using g.u.e.s.s. please choose any four 4 of the problems below to solve. first write out and annotate the problem and then use the g.u.e.s.s. method and show all work. *be aware some of these questions require conversions before they can be solved. do the conversions first before attempting the problem. fyi all units of a particular dimension must match. problems (choose 4) 1. an airplane flies with a constant speed of 720 km/h. how long will it take to travel a distance of 360000 meters? 2. sarah rides her bike with a constant speed of 20 km/h. how long will she take to travel a distance of 10000 meters? 3. bob rides his bike with a constant speed of 10 km/h. how long will he take to travel a distance of 5000 meters? 4. nancy roller skates with a constant speed of 16 km/h. how far can she travel in 30 minutes? 5. nancy rides her horse 36000 m in 120 minutes. what is her average speed in kilometers per hour? 6. a taxi hurries with a constant speed of 88 km/h. how long will it take to travel a distance of 132000 meters? 7. a police car drives with a constant speed of 76 km/h. how long will it take to travel a distance of 38000 meters? 8. juan roller skates with a constant speed of 16 km/h. how far can he travel in 90 minutes?

Explanation:

Step1: Recall the speed - distance - time formula

The formula is $v=\frac{d}{t}$, where $v$ is speed, $d$ is distance and $t$ is time. We can re - arrange it to find $t=\frac{d}{v}$ when we want to find time, and $d = v\times t$ when we want to find distance. Also, convert units as needed ($1\ km = 1000\ m$, $1\ h=60\ min$).

Step2: Solve problem 1

First, convert the distance to kilometers. Since $1\ km = 1000\ m$, then $d = 360000\ m=360\ km$. The speed $v = 720\ km/h$. Using the formula $t=\frac{d}{v}$, we have $t=\frac{360\ km}{720\ km/h}=0.5\ h$.

Step3: Solve problem 3

Convert the distance to kilometers. $d = 5000\ m = 5\ km$. The speed $v = 10\ km/h$. Using the formula $t=\frac{d}{v}$, we get $t=\frac{5\ km}{10\ km/h}=0.5\ h$.

Step4: Solve problem 5

First, convert the distance to kilometers. $d = 36000\ m=36\ km$. Convert the time to hours. Since $1\ h = 60\ min$, then $t = 120\ min = 2\ h$. Using the formula $v=\frac{d}{t}$, we have $v=\frac{36\ km}{2\ h}=18\ km/h$.

Step5: Solve problem 7

Convert the distance to kilometers. $d = 38000\ m=38\ km$. The speed $v = 76\ km/h$. Using the formula $t=\frac{d}{v}$, we get $t=\frac{38\ km}{76\ km/h}=0.5\ h$.

Answer:

1. $0.5\ h$
2. $0.5\ h$
3. $18\ km/h$
4. $0.5\ h$