Mr. Kasberg rides his bike at 6 mph to the bus station. He then rides the bus to work, averaging 30 mph. If he spends 20 minutes less time on the bus than on the bike, and the distance from his house to work is 26 miles, what is the distance from his house to the bus station?
Kinda helpful
bike...d = 6t ... d/6 = t
bus... 26 - d = 30 (t - 1/3)
substituting...26 - d = 30 (d/6 - 1/3)
26 - d = 5d - 10
36 = 6d
Let's assume that the distance from Mr. Kasberg's house to the bus station is x miles.
To find the time it takes for Mr. Kasberg to ride his bike to the bus station, we'll use the equation: Time = Distance / Speed.
The time it takes for Mr. Kasberg to ride his bike is x / 6 hours.
The time Mr. Kasberg spends on the bus is the total time minus the time he spends riding the bike. The total time is (26 / 30) hours.
According to the problem, the time on the bus is 20 minutes less than the time it takes to ride the bike. We need to convert 20 minutes to hours, which is 20 / 60 = 1/3 hour.
Therefore, the equation becomes:
(x / 6) = (26 / 30) - (1 / 3)
Now, we can solve for x.
Multiply the equation by 6 to eliminate the fraction:
6(x / 6) = 6(26 / 30) - 6(1 / 3)
Simplifying, we get:
x = (26 / 5) - 2
The common denominator is 5.
x = (26 - 2(5)) / 5
x = (26 - 10) / 5
x = 16 / 5
So, the distance from Mr. Kasberg's house to the bus station is 16 / 5 miles or 3.2 miles.
To find the distance from Mr. Kasberg's house to the bus station, we can start by finding the total time it takes for his entire trip.
Let's represent the distance from his house to the bus station as d1 (in miles) and the distance from the bus station to work as d2 (also in miles).
Time taken to ride the bike = d1 / 6 hours
Time taken to ride the bus = d2 / 30 hours
Given that he spends 20 minutes less time on the bus than on the bike, we can set up the following equation:
d1 / 6 = (d2 / 30) - (20 minutes / 60 minutes)
Simplifying further,
d1 / 6 = d2 / 30 - 1/3
To solve for d1, we need to find the value of d2. We know that the total distance from his house to work is 26 miles, so we can express this as:
d1 + d2 = 26
Rearranging the equation as d2 = 26 - d1, we can substitute it into the previous equation:
d1 / 6 = (26 - d1) / 30 - 1/3
Now we can solve for d1:
Multiply the equation by the least common multiple, which in this case is 30:
5d1 = (26 - d1) - 10
Multiply out:
5d1 = 26 - d1 - 10
Combine like terms:
6d1 = 16
Divide both sides by 6:
d1 = 16 / 6
Simplifying further,
d1 = 8/3 ≈ 2.67
Therefore, the distance from Mr. Kasberg's house to the bus station is approximately 2.67 miles.