Question

# Zeke ran 4 miles in 45 minutes. If he keeps running at the same pace, how long will it take him to run 10 miles? What is his unit rate in miles per hour?

Solution

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Given that the Zeke ran 4 miles in 45 minutes. So we can find his speed per minute by dividing 4 miles by 45 minutes.

$\Rightarrow$

$\text{speed}=\dfrac{4}{45} \dfrac{\text{miles}}{\text{minute}}$

Now, time taken by him to cover 10 miles can be found out by dividing the distance by his speed.

$\text{time}=\dfrac{\text{distance}}{\text{speed}}=\dfrac{10}{(4/45)}=\dfrac{45\cdot 10}{4}=112.5 \text{ minutes}$

For his unit rate in miles per hour we need to covert given time in hours first. We know that 60 minutes is equal to 1 hour. This implies that 45 minutes is $\dfrac{45}{60}=\dfrac{3}{4}$ hours. So , we can say that Zeke ran 4 miles in $\dfrac{3}{4}$ hours.So we can find his speed in miles per hour by dividing 4 miles by $\dfrac{3}{4}$ hours.

$\Rightarrow$

$\text{speed}=\dfrac{4}{\frac{3}{4}}=\dfrac{16}{3}=5.333 \ \dfrac{\text{miles}}{\text{hour}}$

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