speed and time in travel

Question

In Algebra 1 I am given the following problem:

 

 

Jane jogged to Beth's house at 8 miles per hour and borrowed Beth's scooter, riding back at 20 miles per hour. If the round trip  took 7 hours, how far is it to Beth's house. Write a distance equation with a diagram.

Please help me.

Answer 1

distance = rate*time

distance/rate = time

 

The time it took Jane to jog to Beth's house is distance/(8 mph).  The time it took for her to scooter back is distance/(20 mph).  The sum of the two times is 7 hours:

 

     distance/(8 mph) + distance/(20 mph) = 7 hours

 

Get rid of the denominators by multiplying both sides by 8*20:

 

     20*distance + 8*distance = (7 hours)*8*20

     28*distance = 1120

     distance = 1120/28

     distance = 40 miles

 

That's a LONG jog!

 

Check:

     40/8 = 5 hours to jog to Beth's house

     40/20 = 2 hours to scooter back

     5 hours + 2 hours = 7 hours