Samuel cycled at 10 1/2 miles per hour for 3 1/2 hours. How far did he travel?
To find the distance Samuel traveled, we can multiply his speed in miles per hour (10.5 mph) by the time he traveled in hours (3.5 hours):
Distance = Speed × Time = 10.5 mph × 3.5 hours
Since both the speed and time have fractions, we can first convert them to improper fractions:
Speed = 10 + 1/2 mph = 10 × 2/2 + 1/2 = 20/2 + 1/2 = 21/2 mph
Time = 3 + 1/2 hours = 3 × 2/2 + 1/2 = 6/2 + 1/2 = 7/2 hours
Now, we can multiply the improper fractions to find the distance:
Distance = (21/2) mph × (7/2) hours
Distance = (21 × 7)/(2 × 2) = 147/4
Therefore, Samuel traveled a distance of 147/4 miles, which can also be expressed as 36 3/4 miles.