Bob is going from his house to his uncle Sam's house in another state. He started running. After a while he switches to a bicycle. After a while he switches to a truck. After a while he switches to a sports car. After a while he switches to a helicopter. In each segment he travels twice as fast and for twice the time period of the previous mode of transportation. His total trip's take two hours and four minutes. If he ran at a speed of 15 ft per second. How far is uncle Sam's home.
Let x be the time running, in minutes.
Then 2x, 4x, 8x, and 16x are the times on the bike, truck, car, and helicopter, respectively, in minutes.
Total time = 2 hours and 4 minutes = 124 minutes
x + 2x + 4x + 8x + 16x = 124
x = 4 minutes
4 minutes = 240 seconds
distance to uncle sam's home:
= (15)(240) + (30)(480) + (60)(960) + (120)(1920) + (240)(3840) feet
= ?
To find the distance to Uncle Sam's house, we need to calculate the total distance traveled for each mode of transportation and then add them up.
Let's start by calculating the distance Bob traveled in each segment.
Segment 1: Running
Bob ran at a speed of 15 ft per second. Since we know that speed is equal to distance divided by time, we can rearrange the formula to calculate the distance:
Distance = Speed × Time
Bob ran for twice the time in the previous mode of transportation, which means 2 × 2 minutes and 4 seconds = 4 minutes and 8 seconds.
Converting the time to seconds: 4 minutes × 60 seconds + 8 seconds = 248 seconds
Distance = 15 ft per second × 248 seconds = 3,720 ft
Segment 2: Bicycling
In this segment, Bob travels at twice the speed and for twice the time compared to the previous segment. We know the speed in the previous segment was 15 ft per second, so now Bob is traveling at 2 × 15 ft per second = 30 ft per second.
The time for this segment is twice the time for the previous segment, which is 2 × (4 minutes × 60 seconds + 8 seconds) = 496 seconds.
Distance = 30 ft per second × 496 seconds = 14,880 ft
Segment 3: Truck
Similar to the previous calculations, Bob is now traveling at twice the speed and for twice the time compared to the previous segment.
Speed = 2 × 30 ft per second = 60 ft per second
Time = 2 × (4 minutes × 60 seconds + 8 seconds) = 992 seconds
Distance = 60 ft per second × 992 seconds = 59,520 ft
Segment 4: Sports car
Again, Bob's speed and time double compared to the previous segment.
Speed = 2 × 60 ft per second = 120 ft per second
Time = 2 × (4 minutes × 60 seconds + 8 seconds) = 1,984 seconds
Distance = 120 ft per second × 1,984 seconds = 238,080 ft
Segment 5: Helicopter
For the last segment, Bob will travel at twice the speed and twice the time compared to the previous segment.
Speed = 2 × 120 ft per second = 240 ft per second
Time = 2 × (4 minutes × 60 seconds + 8 seconds) = 3,968 seconds
Distance = 240 ft per second × 3,968 seconds = 947,520 ft
Now, let's add up the distances traveled in each segment to find the total distance to Uncle Sam's house:
Total Distance = Distance in Segment 1 + Distance in Segment 2 + Distance in Segment 3 + Distance in Segment 4 + Distance in Segment 5
Total Distance = 3,720 ft + 14,880 ft + 59,520 ft + 238,080 ft + 947,520 ft
Total Distance = 1,263,720 ft
Therefore, Uncle Sam's house is approximately 1,263,720 ft away from Bob's house.