Question

At noon shawna left her home headed to Rochester, traveling at an average rate of 38 mi/hr. Her brother terrence left 2 hr later, traveling at an average rate of 43 mi/hr, and was 56 mi behind shawna when she arrived in Rochester. How far is it from their home to Rochester, and how long did it take for shawna to make the drive?

Answer 1

The distance between Shawna's Home and Rochester is 228 mi and takes her 6 hr to make the drive.

Explanation:

Known Data

Final distance is the same for both
`x_(f)`, but for Terrence
`x_(f)-56`, due he didn't arrive for 56 mi

Initial distance is the same for both
`x_(i)=0m`

Shawna's Velocity
`v_(S)=38mi/hr`, and time
`t`

Terrence's Velocity
`v_(T)=43mi/hr`, and time, as he starts 2hr later
`t-2`

Formula

`x_(f)=x_(i)+vt`, for both cases

Equation System

Shawna:
`x_(f)=38t` or (1)
`x-38t=0`

Terrence:
`x_(f)-56=43(t-2)`,
`x_(f)-56=43t-86`,
`x_(f)-43t=56-86` and finally (2)
`x_(f)-43t=-30`

By solving this equation system (1) and (2), using any method, we obtain
`x_(f)=228\ mi` and
`t=6\ hr`.