Brian runs 6 miles in 44 minutes. At the same rate, how many minutes would he take to run 9 miles?

Question

Nathan Axel · Accepted Answer

#66#

In situations such as these, it is helpful to establish a ratio, so let's do that!

If we construct a ratio with minutes (time) as the denominator and miles as the numerator, we obtain:

#6/44=9/x#, where #x#= Minutes (time)

We can now cross multiply, which is essentially multiplying in the pattern of an #x#. Here's what I mean:

#color(blue)6/color(red)(44)=color(red)9/color(blue)x#

We will be multiplying the #6# by #x#, and the #44# by #9#. We get:

#6x=396#

We can divide both sides by #6# to get:

#x=66#

Sure, we have an #x# value as our answer, but what does this mean in the context of the problem?

Well, earlier, we defined #x# as being time, or minutes in this situation. In our ratio, it was below #9# miles.

This means it will take Brian #66# minutes to run #9# miles.

Eli Assouline · Answer

undefined To find out how many minutes Brian would take to run 9 miles at the same rate, you can set up a proportion using the ratio of miles to minutes. Since Brian runs 6 miles in 44 minutes, the ratio is 6 miles to 44 minutes. You can then set up the proportion:

6 miles / 44 minutes = 9 miles / x minutes

Cross multiply and solve for x:

6 * x = 9 * 44

Then, divide both sides by 6 to isolate x:

x = (9 * 44) / 6

Calculate the value of x to find out how many minutes it would take for Brian to run 9 miles at the same rate.