Sue was in excellent shape in high school, she could ride her 10-speed bicycle 4.8miles to her grandmother's house in 11 minutes. Her return trip home took 14 minutes. The times are different due to there being a slight downhill slop on part of the trip to her grandmothers. If sue was able to ride her bike on a perfectly flat surgace with no hills, how fast can she travle in miles/hour?
her speed on flat ground --- x mph
effect of hill -------------- y mph
(11/60)((x+y) = 4.8
11x + 11y = 288
(14/60)(x-y) = 4.8
14x - 14y = 288
1st time 14 ---> 164x + 154y = 4032
2nd times 11 --> 154x - 154y = 3168
add them
318x = 7200
x = 22.64
sub into 11x + 11y = 288 to get
y = 3.54
check my arithmetic
To find out how fast Sue can travel in miles per hour, we need to convert the given distances and times to a consistent unit and then calculate her average speed.
First, let's convert the distances from miles to feet, as we will be working with minutes and feet to calculate the speed in miles per hour.
1 mile = 5,280 feet.
Sue's distance to her grandmother's house:
4.8 miles * 5,280 feet/mile = 25,344 feet.
Next, let's convert the time taken for her journey to her grandmother's house from minutes to hours.
11 minutes / 60 minutes/hour = 0.1833 hours.
Now, we can calculate Sue's speed to her grandmother's house:
Speed = Distance / Time
Speed = 25,344 feet / 0.1833 hours ≈ 138,338 feet/hour.
Next, let's convert the distance and time for Sue's return trip home.
Sue's return trip distance:
4.8 miles * 5,280 feet/mile = 25,344 feet (same as before).
Sue's return trip time:
14 minutes / 60 minutes/hour = 0.2333 hours.
Now, we can calculate Sue's speed for her return trip:
Speed = Distance / Time
Speed = 25,344 feet / 0.2333 hours ≈ 108,744 feet/hour.
Finally, to find Sue's speed on a flat surface, we can take the average of the two speeds:
Average Speed = (Speed to Grandmother's house + Speed returning home) / 2
Average Speed = (138,338 feet/hour + 108,744 feet/hour) / 2
Average Speed ≈ 123,541 feet/hour.
To convert this speed from feet per hour to miles per hour:
123,541 feet/hour * (1 mile / 5,280 feet) ≈ 23.42 miles/hour.
Therefore, Sue can travel at approximately 23.42 miles per hour on a perfectly flat surface.