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3 years ago

7

Caroline drove 350 miles to her grandmother’s house. The trip took her 5 1/4 hours. What was her average speed in miles per hour

?

2 answers:

Shalnov [3]3 years ago

7 0

64 hours per hour average
350 miles ÷5.25 hours in which it took= 63.63 rounded is 64 mph average

jok3333 [9.3K]3 years ago

5 0

350/ 5 1/4
350/5.25
66.67
Caroline went 66.67 (or 67 if rounding up) miles per hour.

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Step-by-step explanation:

In this problem we have:

$d_1=1 mi$ is the distance travelled during the 1st day

$d_2=1.3 mi$ is the distance travelled during the 2nd day

$d_3=1.9 mi$ is the distance travelled during the 3rd day

$d_4=3.1 mi$ is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

$d_2-d_1=0.3\\d_3-d_2=2\cdot 0.3 = 0.6\\d_4-d_3=2\cdot 0.6 = 1.2$

Which can be rewritten using the general formula:

$d_{n+1}-d_n=2(d_n-d_{n-1})$

This means that

$d_{n+1}=d_n+2(d_n-d_{n-1})$

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

$d_1=1\\d_2=1.3\\d_3=1.9\\d_4=3.1\\d_5=3.1+2\cdot 1.2=5.5\\d_6=5.5+2\cdot 2.4=10.3\\d_7=10.3+2\cdot 4.8=19.9 mi$

So, the distance travelled on the 7th day is 19.9 miles.

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