You walk at an average of 3.2 miles per hour on the way to school, and at an average of 4 miles per hour on the way home. The total walking time is 18 minutes. How far away is the school? Round your answer to the nearest hundredth of a mile.
Answers
Average walking speed on the way to school =3.2\text {mph}mph
Average walking speed on the way to home =4\text {mph}mph
let total distance from home to school be = \text{D}D
Distance from home to school = distance from school to home
time taken from home to school = \frac{\text{D}}{3.2}
3.2
D
\text{hours}hours
time taken from school to home = \frac{\text{D}}{4}
4
D
\text{hours}hours
Total time taken = 18 minutes = \frac{18}{60}\text{hours}
60
18
hours
\frac{\text{D}}{3.2}
3.2
D
\text{hours}hours + \frac{\text{D}}{4}
4
D
\text{hours}hours = \frac{18}{60}\text{hours}
60
18
hours
\text{D}(\frac{1}{3.2}+\frac{1}{4})=\frac{18}{60}D(
3.2
1
+
4
1
)=
60
18
\text{D}\frac{9}{16}=\frac{18}{60}D
16
9
=
60
18
\text{D}=\frac{32}{60}D=
60
32
\text{miles}miles
\text{D}=0.53D=0.53 \text{miles}miles
The school is 0.530.53 \text{miles}miles from home