Question

Jeff was already 7 miles out of town when his sister
started after him on her bicycle. Jeff's rate was 2.5
miles per hour and his sister's rate was 6 miles per hour. How long did it take Jeff's sister to catch up to Jeff?

Answer 1

The sister catches up Jeff after 2 hours

Step-by-step explanation:

We can write Jeff's position and his sister position at time t using the following expressions:

- Jeff position:

$x_j(t) = 7 + 2.5 t$

where:

7 is the initial position of Jeff when his sister sarts chasing him

2.5 is Jeff's velocity (in miles/hour), so its position increases by 2.5 miles for each hour

t is the time measured in hours

- Sister position:

$x_s(t) = 6t$

where

6 is the sister velocity (her position increases by 6 miles for every hour)

t is the time measured in hours

The sister catches up Jeff when the two positions are equal, so

$x_j(t) = x_s(t)\\7+2.5t=6t$

And solving for t,

$7+2.5t-2.5t=6t-2.5t\\7=3.5t\\t=\frac{7}{3.5}=2 h$

So, the sister catches Jeff after 2 hours.

Learn more about speed:

brainly.com/question/8893949

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