Question

I have a a Math Vocabulary problem. I have a word bank of vocabulary. Here is the question. Eli runs a distance of 3 miles in 2/5 of an hour. Jess runs a distance of 4/5 mile in 1/10 of an hour. Who had the faster speed? Show your work.And on the right side of my paper i have a word bank with fill in theblanks

Answer 1

I can find the unit rate of miles per hour for each runner.

The ratio of distance to time for Eli is 3 miles to (2/5) hour

I can write this as a fraction: (3) / (2/5)

I can do the same form Jess's distance to time: (4/5) / (1/10)

Both of these are fractions because the numerator, denominator, or both are fractions.

I can simplify the fractions by dividing the numerator by denominator.

I write each as a divsion expression and find the quotient by multiplying the inverse.

3 ÷ (2/5)

= 3 × (5/2)

= (15/2)

= 7.5

(4/5) ÷ (1/10)

(4/5) × (10/1)

= (40/5)

= 8

The unit rate for Eli is 7.5 miles per hour. The unit rate for Jess is 8 miles per hour.

The faster speed is the one with the 8 unit rate.

The runner with the faster speed is Jess.

Step-by-step explanation

We will quickly calculate their speeds and compare before answering the questions.

Speed = (Distance/Time)

For Eli,

Speed = 3 ÷ (2/5)

Noting that the division involving fractions are solved by changing the division sign into multiplication sign and the fraction after the sign changes to its reciprocal or its inverse.

Speed = 3 × (5/2) = (15/2) miles per hour = 7.5 miles per hour

For Jess,

Speed = (4/5) ÷ (1/10)

Speed = (4/5) × (10/1)

Speed = (40/5) miles per hour = 8 miles per hour

Hope this Helps!!!