Jessica can jog to work in 4/5 of an hour. When she rides her bike, it takes her 3/10 of an hour. If she rides 10 miles per hour faster than she jogs, how far away is her work?
She bikes at speed b, so d/b = 3/10
She jogs at speed j, so d/j = 4/5
But, b=j+10 so,
d/(j+10) = 3/10
d/j = 4/5
d = 3/10 (j+10) = 4j/5 = 8j/10
3(j+10) = 8j
30 = 5j
j=6
b=16
d=24/5 mi
To find the distance to Jessica's work, we need to determine the speed at which she jogs and rides her bike.
Let's start by converting the given times into minutes for easier calculation. We know that Jessica jogs in 4/5 of an hour, which is (4/5) * 60 = 48 minutes. We also know that she rides her bike in 3/10 of an hour, which is (3/10) * 60 = 18 minutes.
Now, let's assume that Jessica's jogging speed is x miles per hour. We are told that when she rides her bike, she goes 10 miles per hour faster than when she jogs. So her biking speed would be (x + 10) miles per hour.
To calculate the distance, we need to use the formula: distance = speed * time.
For jogging: distance = x * 48 minutes
For biking: distance = (x + 10) * 18 minutes
Since the distances for jogging and biking are the same (as it is her work distance), we can set these two equations equal to each other:
x * 48 = (x + 10) * 18
Now we can solve this equation to find the jogging speed (x) and, subsequently, the distance to Jessica's work.
48x = 18(x + 10)
48x = 18x + 180
48x - 18x = 180
30x = 180
x = 180 / 30
x = 6
This means that Jessica's jogging speed is 6 miles per hour. And since her biking speed is 10 miles per hour faster, her biking speed is 6 + 10 = 16 miles per hour.
Now we can calculate the distance to her work using either the jogging or biking speed. Let's use the jogging speed for consistency.
distance = speed * time
distance = 6 miles per hour * 48 minutes
distance = (6 / 60) * 48 miles
distance = 4.8 miles
Therefore, Jessica's work is 4.8 miles away.