# Distance/Rate/Time equation

• Feb 8th 2011, 12:52 PM
gurrry
Distance/Rate/Time equation
Last question of the day, I promise! lol...

I am having a real hard time translating word problems having to do with distance and time. I dont understand the concept of it for some reason.. The problem I am trying to solve is this:

"On a 300 mile trip to Chicago, Josh drove part of the time at 60 mph and the remainder of the trip at 70 mph. If the total trip took 4.5 hours, for how many miles did Josh drive at a rate of 60 mph?"

Can someone teach me how you are supposed to set these problems up? My teacher gave us the equation 60x + 70(4.5 - x) = 300, but I dont understand how we get there.

why are we subtracting 4.5 (time) from the miles driven (x)? I dont get it...
• Feb 8th 2011, 12:55 PM
janvdl
Quote:

Originally Posted by gurrry
Can someone teach me how you are supposed to set these problems up? My teacher gave us the equation 60x + 70(4.5 - x) = 300, but I dont understand how we get there.

why are we subtracting 4.5 (time) from the miles driven (x)? I dont get it...

4.5 hours was the total time. $x$ is the number of hours Josh drove at 60. For the remainder of the 4.5 hours he drove 75, i.e. $(4.5 - x)$.
• Feb 8th 2011, 01:00 PM
gurrry
Ok.. so then you just solve for X, (which is 1.5)

then multiply that by 60 because you are just trying to find out how many miles he drove at 60... which becomes 90 miles..

I think I understand somewhat better now.. thanks for the help
• Feb 8th 2011, 04:49 PM
Wilmer
Since time = distance/speed, you can also go this way:
Let x = distance @ 60
x/60 + (300-x)/70 = 4.5
x = 90
• Feb 9th 2011, 03:23 AM
HallsofIvy
Quote:

Originally Posted by gurrry
Last question of the day, I promise! lol...

I am having a real hard time translating word problems having to do with distance and time. I dont understand the concept of it for some reason.. The problem I am trying to solve is this:

"On a 300 mile trip to Chicago, Josh drove part of the time at 60 mph and the remainder of the trip at 70 mph. If the total trip took 4.5 hours, for how many miles did Josh drive at a rate of 60 mph?"

Can someone teach me how you are supposed to set these problems up? My teacher gave us the equation 60x + 70(4.5 - x) = 300, but I dont understand how we get there.

why are we subtracting 4.5 (time) from the miles driven (x)? I dont get it...

What your teacher gave you makes NO SENSE unless you also know what the "x" represents. Never learn a formula without understanding what the various variables mean. When you ask "why are we subtracting 4.5 (time) from the miles driven (x)?" you are showing some talent for logical thinking! You cannot subtract distance from time- that makes no sense. Your error is in thinking that "x" is distance. The only way it would make sense to have "4.5 hours- x" is if x itself is in hours- that is, x must be the time Josh drives at 60 mph, not the distance. If Josh drives at 60 mph for x hours, then there are 4.5- x hours when he must have been driving at 70 mph.

At 60 mph for x hours, Josh drove 60x miles. At 70 mph for 4.5- x hours, Josh drove 70(4.5- x) miles. Putting those together, Josh drove 60x+ 70(4.5- x) miles and we are told that he drove 300 miles: 60x+ 70(4.5- x)= 300. Once you have solve for x in hours, multiply by 60 mph to find the number of miles he drove.

I strongly recommend that, for any problem like this, when you write out an equation, explicitely write out what any variables in that equation recommend. For this problem you should have written out clearly "x is the time, in hours, that Josh drove at 60 mph". That will help you keep track of what you are doing (and really shock your teacher).