When Sarah takes the bus to work, the trip takes 30 minutes. When she takes the train to work, the trip takes 20 minutes. The average speed to the train is 15 mph faster than the speed of the bus. Find the distance to work.
30 mt
time taken to travel by bus= 30 min = 1/2 hour
time taken to travel by train = 20min = 1/3 hour
let the speed of bus be = x mph
then speed of the train = (x+15) mph
speed = distance/time
let the distance to work be y metres
then,
distance= speed*time
1/2*x=1/3*(x+15)
x=30mph
now
distance=y= speed of bus*time
y= 30*1/2=15mt
Let's assume the speed of the bus is x mph.
Given that the average speed of the train is 15 mph faster than the speed of the bus, the speed of the train is (x + 15) mph.
The time taken by the bus to travel to work is 30 minutes, which is equivalent to 30/60 = 0.5 hours.
Similarly, the time taken by the train to travel to work is 20 minutes, which is equivalent to 20/60 = 0.33 hours.
We can use the formula distance = speed * time to find the distances.
For the bus: distance_bus = x mph * 0.5 hours
For the train: distance_train = (x + 15) mph * 0.33 hours
Since the distance to work is the same for both modes of transportation, we have:
x * 0.5 = (x + 15) * 0.33
Now, let's solve the equation:
0.5x = 0.33(x + 15)
0.5x = 0.33x + 4.95
0.17x = 4.95
x = 4.95 / 0.17
x ≈ 29.12 mph
Now, we can find the distance to work using either the distance_bus or distance_train formula:
distance_bus = 29.12 mph * 0.5 hours
distance_bus ≈ 14.56 miles
Therefore, the distance to work is approximately 14.56 miles.
To find the distance to work, we can set up a system of equations based on the information given.
Let's assume the speed of the bus is x mph. Therefore, the speed of the train is x + 15 mph.
We know that time is equal to distance divided by speed. So, we can set up two equations:
For the bus: time = distance / speed
30 minutes = distance / x (since the speed of the bus is x mph)
For the train: time = distance / speed
20 minutes = distance / (x + 15) (since the speed of the train is x + 15 mph)
Now, we can solve the two equations to find the distance.
Multiplying both sides of the first equation by x, we get:
30x = distance
Multiplying both sides of the second equation by (x + 15), we get:
20(x + 15) = distance
Since we are looking for the distance to work, which is the same in both cases, we can set the two equations equal to each other:
30x = 20(x + 15)
Now, we can solve for x:
30x = 20x + 300
10x = 300
x = 30
Therefore, the speed of the bus is 30 mph, and the speed of the train is 45 mph.
Now we can find the distance by substituting the value of x back into one of the equations:
distance = 30x = 30 * 30 = 900 miles
So, the distance to work is 900 miles.