Question

Brothers, Paul and Pete, walk 2 miles to school from home. Paul can walk to school in 24 minutes. Pete has slept in again and needs to run to school. Paul walks at constant rate, and Pete runs at a constant rate. The graph of the function that represents Pete's run is shown below. Which brother is moving at a greater rate? Explain how you know. If Pete leaves 5 minutes after Paul, will he catch Paul before they get to school?

Answer 1

1) Gathering the data from the question

Paul and Pete walk 2 miles

Paul can make it in 24 min

Pete's run in on the graph

a) The graph is in miles per hour

Converting Paul's speed:

1h 60 min

x 24

x=24/60 x =0.4 hours

24 min = 0.4 hours

V = 2/ 0.4 V paul = 5 mph

Picking the points, Pete 8 mph ( 1,8)

So, Pete is at a greater rate 8mph, because at t= 1 hour y = 8 miles

b) The distance to the school is 2 miles.

In 5 minutes = 1/12 Paul has walked:

5 =d/1/12

So in 5 minutes, Paul has walked 0.83 miles.

If Pete is running at 8 mph, He'll end up reaching Paul.

We

5/6=8x

5=48x

x= Paul will reach Pete in approximately 6 minutes, and eventually before they get to school

x=