calculate the speed of the cyclist, we need to divide the distance traveled (3 3/4 miles) by the time taken (3/10 hours). Let's convert the mixed number to an improper fraction first
3 3/4 miles = (4 * 3 + 3) / 4 = 15/4 miles
Now we can calculate the speed:
Speed = distance / time
Speed = (15/4 miles) / (3/10 hours)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Speed = (15/4 miles) * (10/3 hours)
Simplifying the fractions:
Speed = (15 * 10) / (4 * 3) miles/hour
Speed = 150/12 miles/hour
Simplifying the fraction further:
Speed = 12.5 miles/hour
So, the cyclist was going at a speed of 12.5 miles per hour.