Question

Rachel ran from her house to school at an average speed of 6 miles per hour and returned along the same route at an average speed of 4 miles per hour. If the total time it took her to run to the school and back was one hour, how far is it from Rachel’s house to school?

Answer 1

Answer:

2.4 miles

Step-by-step explanation:

Let the distance from Rachel's school to her home be m miles.

She ran from her house to school at an average speed of 6 miles per hour. Let the time she took to go from house to school is $t_{1}$

Since,

Distance = Speed  x Time

m = 6$t_{1}$

or

$t_{1}$ = $\frac{m}{6}$ miles

Rachel returned to her house with an average speed of 4 miles per hour. Let the time she took from school to house is $t_{2}$. Using the same formula again, we get:

m = 4$t_{2}$

or

$t_{2}$ = $\frac{m}{4}$ miles

Since, the total time she tool to run to and back from the school is 1 hour, we an write:

Total time = $t_{1}+t_{2}$

$1=\frac{m}{6} +\frac{m}{4}\\\\ 1=\frac{4m+6m}{24}\\\\ 24 = 10m\\\\ m = 2.4$

Since, m represents the distance from Rachel's school to her house, we can conclude that Rachel's school is 2.4 miles far from her house.