Mathematics: Fred walked a trail at 2 mph. paul started 30 minutes later on the same trail and walked at a pace of 3 mph. create a system of equations in which y represents the distance walked in miles and x represents the time walked in hours. explain what this solution means in terms of paul catching up to fred.

Fred walked a trail at 2 mph. paul started 30 minutes

Ответ:

clipsyden

14.01.2022

Mathematics

$y=2x\\y=3(x-\frac{1}{2})$

Paul will catch Fred after $1\ hours$ at a distance $3\ miles$ .

Step-by-step explanation:

Distance is represented by and the time is represented by . Here after hours(when Fred started) the distance covered by Fred and Paul is same that is .

For Fred:

time=

distance=

Speed $=2\ mph$

$Distance=speed\times time\\y=2\times x \\y=2x$

Paul:

Since Fred started 30 minutes earlier, so Paul's travel time will be 30 minutes less than that of Fred.

Time $=x-\frac{1}{2}$

Speed $=3\ mph$

Distance $=y\\$

$y=3\times (x-\frac{1}{2})\\y=3(x-\frac{1}{2})$

Hence system of equation

$y=2x\\y=3(x-\frac{1}{2})$

Solution of this system of equations gives the time, when Paul will catch Fred and distance covered by each of them.

$y=2x\\y=3(x-\frac{1}{2})\\\\2x=3x-\frac{3}{2}\\x=\frac{3}{2}\\\\y=2x\\y=2\times \frac{3}{2}\\y=3$

Time taken by Paul $=x-\frac{1}{2}=\frac{3}{2}-\frac{1}{2}=1$

Hence Paul will catch Fred after $1\ hours$ at a distance $3\ miles$ .

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