what is the distance between the two points?

Question

A jogger runs from point A to point B at 10 miles per hour. The jogger returns from point B to point A at 6 miles per hour. If the trio took 1 hour and 36 minutes, what was the distance between the two points? 

Answer 1

Hey Annie!

 

You could do it this way too.

 

This is a THERE and BACK problem.

 

Let x represent the distance between points A and B.

 

Make a Chart.

 

Column #1 would be the RATE column

Column #2 would be the TIME column

Column #3 would be the DISTANCE column

 

Row #1 would be the THERE row

Row #2 would be the BACK row

 

So the chart would look like this:

 

                      RATE              TIME               DISTANCE

 

THERE             10                                             x         

 

BACK                6                                             x

 

To fill in the TIME column just divide the DISTANCE by the RATE

 

So  the chart would now look like this:

 

                    RATE              TIME               DISTANCE 
THERE             10                x/10                     x         
 
BACK                6                x/6                       x

 

 

The equation will come from the TIME column.

 

Time THERE plus Time BACK equals 1.6 hours  ( 1 hour and 36 minutes = 1.6 hours )

 

 

So,     x/10  + x/6   = 1.6

 

Solve this equation by multiplying each term on both sides by 60.

 

So the equation becomes    6x + 10x = 96

 

Solve the equation   and    x = 6

 

Which is the distance between the point A and B,   6 miles !

 

 

Happy days.

 

 

Answer 2

Answer is 6 miles..... 36 minutes to get there and 1 hour to get back.

 

10x=6(1.6-x)

x=.6 of an hour to run at 10 mph

therefore he ran 6 miles one way