1.

Paula jogged for a total of 30 minutes. Her average speed for the first 10 minutes was 5 miles per hour. During the remainder of her time, she jogged 2.5 miles. What was Paula's average for her entire jog ?

Answer»

`6(1)/(2)` mph
`6(2)/(3)` mph
`7(1)/(2)` mph
`7(1)/(3)` mph

Solution :You need to figure out the total distance TRAVELED so that you can computer her overall average RATE. Since her jog lasted 30 minutes overall, we can already plug total time into the formula : `"rate"=("distance")/("time")`. Since the question asks for a rate in miles per hour, we need to convert minutes to hours , 30 minutes equals `(1)/(2)` hor.During the first 10 minutes, or the first `(1)/(6)` hours, Paula jogged at five miles per hour. That means that she jogged `(5)/(6)` miles. She then jogged 2.5, or `(5)/(2)`, miles.
`(5)/(6)+(5)/(2)=(5)/(6)+(15)/(6)=(20)/(6)`
So Paula jogged a total of `(20)/(6)("or " 3(1)/(3))` miles. Now divide this distance by the time.
`((20)/(6))/((1)/(2))=(20)/(6)xx2=(40)/(6)`
So Paula jogged at an overall average rate of `(40)/(6)`, or `6(2)/(3)`, miles per hour.


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