Mr. Pillot always rides his bicycle to work, and he begins his ride at the same time every day. If he averages 10 miles per hour, he arrives at work 2 minutes late, but, if he averages 15 miles per hour, he arrives 1 minute early. How many miles does Mr. Pillot ride to work? Express your answer as a decimal to the nearest tenth.

10 miles per hours = 1/6 miles per minute

15 miles per hours=1/4 miles per minute

Now, assume he need x minute to rides his bicycle to work.

if he averages 10 miles per hour, then he need (x+2) minute to arrives at work

if he averages 15 miles per hour, then he need (x-1) minute to arrives at work

distance equal velocity multiply by time. d=v*t

distance did not change, so we can set up an equation like ...

1/6 * (x+2) = 1/4 * (x-1)

x+2=1.5 (x-1)

x+2=1.5x-1.5

0.5x=3.5

x=7

If if he average speed is 15 miles per hour (1/4 miles per minute), he need 7-1=6 minute to arrive at work

6 * (1/4) = 3/2 miles=1.5 miles

Same, If he average speed is 10 miles per hour (1/6 miles per minute), he need 7+2=9 minute to arrive at work.

9 * (1/6) = 3/2 miles=1.5 miles (I just checking)