SOLUTION: brice left home and ran to school at 10 mi/hr. he ran back at 8 mi/hr. the entire trip took 27 min. How far did he run? Make a chart

Question 166507: brice left home and ran to school at 10 mi/hr. he ran back at 8 mi/hr. the entire trip took 27 min. How far did he run? Make a chart
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The goal of this problem is to find the distance "d" of

Let t=time it took to get to school

So this means that it took minutes to get home

Now convert 10 mi/hr to mi/min to get mi/min. So going to school, he's running mi/min (or in decimal form 0.1667 mi/min)

Now convert 8 mi/hr to mi/min to get mi/min. So coming home, he's running mi/min (or in decimal form 0.1333 mi/min)

Direction	Distance	Rate/Speed	Time
Going to School	d miles	1/6 mi/min	t min
Coming Home	d miles	2/15 mi/min	27-t min

Going to School:

Start with the distance rate time formula

Plug in

------------------

Coming Home:

Start with the distance rate time formula

Plug in and replace "t" with

Now plug in (the "going to school" equation)

Multiply both sides by the LCD 30 to clear out the fractions.

-----------------------------------

Distribute.

Add to both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

So he took 12 minutes to get to school.

Go back to the first equation

Plug in

Multiply

Reduce

So the distance from his home to school is 2 miles. Now since he went to school and came home he traveled that distance twice. So this means that he traveled a total distance of 4 miles
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