Can you help me set this up?
Mr. Smith could ride his 10-speed bike 4.8 miles to his mom's house in 11 minutes. His return trip home took 14 minutes. The times are different due to there being a slight downhill slope on part of the trip to his mom's house. If Mr. Smith was able to ride his bike on a flat surface with no hills, how fast can he travel in miles/hour?
Thank you!!!!
the distance is the same
distance = speed * time
if the bike's flat-land speed is b, and the drag caused by the uphills slope is s,
11/60 (b+s) = 4.8
14/60 (b-s) = 4.8
b = 23.38 mph
Sure, I can help you with that!
To find the speed at which Mr. Smith can travel on a flat surface with no hills, we need to convert the given times into hours and then use the formula for speed, which is Distance/Time.
First, let's convert the given times from minutes to hours.
Mr. Smith took 11 minutes to ride to his mom's house. To convert this to hours, we divide 11 by 60 (since there are 60 minutes in an hour):
11 minutes ÷ 60 minutes/hour = 0.1833 hours (rounded to four decimal places).
Similarly, Mr. Smith took 14 minutes to return home. To convert this to hours, we divide 14 by 60:
14 minutes ÷ 60 minutes/hour = 0.2333 hours (rounded to four decimal places).
Now, let's calculate the speed for each leg of the trip.
Speed = Distance/Time.
For the trip to his mom's house:
Distance = 4.8 miles.
Time = 0.1833 hours.
Speed to his mom's house = 4.8 miles / 0.1833 hours = 26.1932 miles/hour (rounded to four decimal places).
For the return trip home:
Distance = 4.8 miles.
Time = 0.2333 hours.
Speed on the return trip = 4.8 miles / 0.2333 hours = 20.581 miles/hour (rounded to three decimal places).
Since the speed on the return trip is slower than the speed to his mom's house, we can assume that the downhill slope on the way to his mom's house made him faster.
Therefore, the speed at which Mr. Smith can travel on a flat surface with no hills is the slower speed of 20.581 miles/hour.
So, Mr. Smith can travel at a speed of approximately 20.581 miles/hour on a flat surface with no hills.
I hope this explanation helps you! If you have any further questions, feel free to ask.