Question

Brianna left the bookstore traveling 32 mph. Then 3.2 hours later, Sonya left traveling the same direction at 44.8 mph. How long until Sonya catches up with Brianna

Answer 1

8 hours

Explanation:

Let t hours be the time needed Sonya to catch up Brianna.

Sonya:

Time = t hours

Rate = 44.8 mph

Distance
`=D_S` miles

Brianna

Time
`=t+3.2` hours

Rate = 32 mph

Distance
`=D_B` miles

Note that
`D_S=D_B,` because Sonya must catch up Brianna.

Use formula
`D=r\cdot t`

Hence,

`44.8t=32(t+3.2)`

Solve this equation:

`44.8t=32t+32\cdot 3.2\\ \\44.8t-32t=102.4\\ \\12.8t=102.4\\ \\t=8`