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

2.4 miles

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)` =
`(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)` =
`(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=(m)/(6) +(m)/(4)\\\\ 1=(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.