A car traveled 3⁄4 mile in one minute at constant speed. What was the speed of the car in miles per hour?
2 answers:
the fractions are set up so minutes cancel out
multiply the numerators to get 45 miles
multiply the denominators to get 1 hour
45 miles per hour
hope this helped
Distance traveled by car in one minute = 3/4 mile
The relation between hour and minutes is given by:
one hour = sixty minutes
one minute = 1/60 hours
so we can replace one minute by 1/60 hours
Distance traveled by car in one minute =3/4 mile
Distance traveled by car in 1/60 hour =3/4 miles
distance traveled by car in 1 hour = (3/4) ÷(1/60)
In division we take reciprocal of the number after division sign and multiply it with first.
Reciprocal of 1/60 is 60
so multiplying 3/4 and 60
So distance traveled by car in one hour is 45 miles.
Speed of car is 45 miles per hour .
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<em>Comment on simplifying rational expressions</em>
Division of fractions works the same whether you're working with numbers or polynomials (or anything else). Dividing by something is the same as multiplying by its inverse (reciprocal).
(a/b)/(c/d) = (a/b)·(d/c)
I learned this as "invert and multiply". I've recently seen it referred to as "copy dot flip", meaning you copy the numerator, use a dot symbol to indicate multipication, then flip the denominator (make its reciprocal) to become what you're multiplying by.