Tricky Math Problem?

Test Preparation
1

<p>Marco drove from home to work at an average speed of 50
miles per hour and returned home along the same route at an
average speed of 46 miles per hour. If his total driving time for
the trip was 4 hours, how many minutes did it take Marco to
drive from work to home?</p>

<p>I got the answer to be 115 and here's how I did it
50x=46(4-x)
x=184/96 </p>

<p>Thats the speed from work to home in hours, and then u mutiply by 60 to get speed in minutes</p>

<p>The book said the answer was 125. How?</p>

2

<p>Set up a proportion. </p>

<p>The slower time (46 mph) takes 50/46 as long to travel any route that you would’ve traveled at 50 mph. That reduces to 25/23. This means that the ratio for time travelling a distance at 46 mph to that of 50 mph is 25:23. Therefore, divide 240 minutes (4 hours) by 48 to get 5. You want to see how long the 46 mph leg took, so multiply 25(5), and boom</p>

<p>125 minutes</p>

3

<p>Dumb, lol that is reallly logical, but can you point out what I did wrong in my setup?</p>

4

<p>Your equation is almost correct. You actually found the time for the ride there rather than home. The equation should simply be:</p>

<p>50(4-x)=46x</p>

<p>Using that equation and then multiplying by 60 will get you 125 minutes.</p>

<p>Actually it would be much simpler to make the equation into:</p>

<p>50(240-x)=46x</p>

<p>that way you don’t have to remember to do any additional steps</p>

5

<p>I still don’t get it. It says Marco went from home to work at 50 miles per hour and returned back at 46 mph. The question asks how many minutes did it take to take Marco to go from home to work, so wouldn’t that be asking for the 50 * x? I’m having trouble with the setup; how do you know that the 4-x goes on the 50 and not the 46?</p>

6

<p>In your equation, x is defined to represent the time such as 50*x= the distance travelled
of course, you know that 50mph is faster than 46mph, so it would take less time to travel… </p>

<p>(Stop, let’s be serious)
Let y be the time a car take with a speed of 46mph.
x+y=4 <=>y=4-x
In other words, x represent the time marco took from home to work.
y represent the time marco took from work to home.
You correctly noticed that 50<em>x=46</em>y
However you’re asked to find y, not x.
x=115min and y=4-x<=>y=125</p>

<p>In fact, you could have avoided this last step by simply defining x to represent the time such as 46x= the distance travelled</p>

<p>DUMBLETHAL:
why dividing by 48?</p>

7

<p>Bump intrested to find out </p>

<p>Sent from my HTC VLE_U using CC</p>

8

<p>I agree with 075014.</p>

<p>Which time are you trying to find? In the original post you wrote, “how many minutes did it take Marco to drive from work to home?”</p>

<p>In your last comment you wrote, “how many minutes did it take to take Marco to go from home to work.”</p>

<p>First, find out which one you are really looking for. Home -> work? Or work -> home? IF you are looking for the minutes from work to home like in the original post, here is how you find 125 minutes:</p>

<p>50x (where x is the time in hours) is going to WORK, and 46(4-x) is going HOME. Everything you did to find x is correct. Now you want to find 4-x.</p>

<p>You got 184/96 as x. </p>

<p>Time going home=
4 - (184/96)
384/96 (equivalent to 4) - (184/96) = 200/96</p>

<p>200/96 * by 60 (to make it in minutes) is 125 minutes.</p>

9

<p>

The ratio of the times reduced to 25:23. Meaning if you had 48 parts (25+23) then 25 are one and 23 are the other. Since you have 240 parts (minutes), 240*(25/48) gives you 125 minutes.</p>