Word math is so hard please help

Question

Frank Frank runs 4 miles in 30 minutes at the same rate how many miles would he run in 48 minutes

Answer 1

Key words here are "at the same rate". A rate can be represented as a proportion - in this case, a proportion of distance traveled to minutes elapsed. So, we can depict this problem as a proportion:

4 miles / 30 minutes = x miles / 48 minutes

-or-

4 / 30 = x / 48

You can then solve that by finding the cross product:

4 * 48 = x * 30

...and then solving for x:

192 = x * 30

192 / 30 = x

x = 6.4

____

At least, that's how you're supposed to answer this problem. But I skipped over the hard part, how I reasoned out a way to solve this. So, let me start over and address that.

Frankie Frank is able to run 4 miles in 30 minutes. They're describing this as being a 'rate', but a more familiar term would work better here - 'speed'.

You're familiar with miles per hour, often given as 'mph'? You see it on freeway signs, right? "SPEED LIMIT 60 MPH." That means your car should only be moving fast enough to cover 60 miles in the span of one hour.

So, if you want to see how far your car would travel at 60 MPH for 2 hours, you would cover 120 miles, right? That just makes sense - you'd travel 60 miles the first hour, then travel 60 more the second hour. If you're only traveling for half an hour, you'd only cover half of 60 miles, which is 30.

You can represent both scenarios with 60*2=120 and 60*(1/2)=30, respectively. It's a pretty simple setup - you multiply the speed by the time traveled to get the distance traveled.

This can be applied to our problem, too. If Frankie Frank runs 4 miles in 30 minutes, then how many miles (or rather, what fraction of a mile) can he run in one minute? I can represent that like so:

(the speed) * 30 minutes = 4 miles

This time, we need to do this multiplication problem in reverse, and you know what that means - division!

4 / 30 = (the speed)

We can just represent the answer as a fraction: 4/30 (which is 2/15 after you simplify it). Frankie Frank can run 4/30ths of a mile in a minute. That's Frankie Frank's speed! Now we can just take that speed and figure out how many miles he would run if you let him loose for 48 minutes:

4/30 * 48 =

192/30 =

32/5 = 6 2/5 -or- 6.4

And that is how I would reason out this problem!