Amy and Ashley bike along the same trail. Amy bikes the entire trail at a speed of 20 mph and Ashley bikes it at a speed of 15 mph. Amy finishes biking the entire trail 8 minutes before Ashley.
How many miles long is the bike trail?
length of trail ---- x miles
x/15 - x/20 = 8/60
times 60 , the LCD
4x - 3x = 8
x = 8
the trail is 8 miles long
check:
time at 20 mph = 8/20 hrs = 24 minutes
time at 15 mph = 8/15 hrs = 32 minutes
for a difference of 8 minutes
To find the length of the bike trail, we can start by calculating the time it takes for each person to bike the trail.
Let's denote the length of the bike trail as 'x' miles.
Amy's speed is 20 mph, so her biking time is given by: Time = Distance / Speed.
Amy's time = x miles / 20 mph = x/20 hours.
Ashley's speed is 15 mph, so her biking time is given by: Time = Distance / Speed.
Ashley's time = x miles / 15 mph = x/15 hours.
Since Amy finishes biking 8 minutes (which is 8/60 hours) before Ashley, we can write the following equation:
Amy's time = Ashley's time + 8/60 hours.
Substituting the values, we get:
x/20 = x/15 + 8/60.
To simplify the equation, we can multiply through by a common multiple of the denominators (60 in this case) to get rid of the fractions:
3x = 4x + 8.
Now, we can solve for x:
4x - 3x = 8,
x = 8.
Therefore, the bike trail is 8 miles long.