Distance Systems

Question

Rubio started home from school riding his bike at 14 mph. Part way home he hit a pothole and got a flat tire and he walked his bike the rest of the way home at 2 mph. It took him an 1 hour and 30 minutes to get home. If he lives 9 miles from school, for how many minutes did he ride?

Answer 1

We will use the distance formula

 

d = vt

 

where:

d = distance (in miles)

v = speed (in mph)

t = time (in hours)

 

 

Write down what we know:

d_total = 9 miles

v_ride = 14 mph

v_walk = 2 mph

t_total = 1 hour + 30 minutes = 1 hour + 0.5 hour = 1.5 hours

 

What we need to find out:

t_ride

 

 

Note: If you cannot see the subscripts, you can increase your computer's screen size.

 

 

Then, we use a variation of the distance formula so that it consists of all the variables listed above.

 

d_total = d_ride + d_walk

 

d_total = (v_ride * t_ride) + (v_walk * t_walk)

 

 

Next, we use the fact that

 

t_ride + t_walk = 1.5   --->  equation for total time

 

Rearranging, we can get

 

t_ride = 1.5 - t_walk

 

 

Substitute the known values and the equation for time into the variation of the distance formula.

 

 

9 = 14(1.5 - t_walk) + 2(t_walk)

 

 

Solve for t_walk .

 

9 = 21 - 14t_walk + 2t_walk

 

-12 = -12t_walk

 

1 = t_walk

 

 

Substiute this value of t_walk into the time equation to solve for t_ride.

 

t_ride = 1.5 - 1

 

t_ride = 0.5

 

 

He rode for 0.5 hours.  So he rode for 30 minutes.