word problem

Question

Lori recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 10 miles per hour faster than on her way home. If Lori spent a total of 1 hour bicycling, find the two rates.

Answer 1

Let x = speed on her way home

 

Then x+10 = speed on her way there

 

Distance = (Rate)(Time), so Time = Distance/Rate

 

Total Time = 1

 

12/x + 12/(x+10) = 1

 

Multiply both sides by x(x+10):  12(x+10) + 12x = x(x+10)

 

                                              24x + 120 = x² + 10x

 

                                              x² - 14x - 120 = 0

 

                                              (x - 20)(x + 6) = 0

 

                                               x = 20 or x = -6

 

Since x can't be negative, x = 20 mph

 

Lori traveled 20 mph on her way home and 30 mph on her way there.

Answer 2

We can figure this out be setting up an equation. We know that the total distance traveled is 24 miles (22 miles each way). because sge traveled for exactly one hour that means she traveled 24 miles in 1 hour, so we are looking for how fast she went in each direction. 

 

Our hint is that she went 10mph faster going to her friend's house. So we can set up the equation. X is the base # they share, and we need to find it to figure out the rates.

 

(x+10) +x=24. Subtract 10 from both sides we get x+x=14 simplify this we get 2x=14 Divide each side by 2 and we have the value of X. x=7 

 

going back to our initial conclusions: the rate of the speed to the friends house was x+10. So 7+10 which equsls 17mph. The rate of her speed back home was just x, so 7mph. 

 

 

To check add 7+17 abd we get 24 mph whic is what she traveled.